In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and Ri is a ring for every i in I, then the cartesian productΠi ∈ IRi can be turned into a ring by defining the operations coordinate-wise.
The resulting ring is called a direct product of the rings Ri. The direct product of finitely many rings coincides with the direct sum of rings.
If R = Πi ∈ IRi is a product of rings, then for every i in I we have a surjectivering homomorphismpi: R → Ri which projects the product on the ith coordinate. The product R, together with the projections pi, has the following universal property:
This shows that the product of rings is an instance of products in the sense of category theory. However, despite also being called the direct sum of rings when I is finite, the product of rings is not a coproduct in the sense of category theory. In particular, if I has more than one element, the inclusion map Ri → R is not ring homomorphism as it does not map the identity in Ri to the identity in R.
Lec - 20 DIRECT PRODUCT RINGS II (Z/2Z) X (Z/3Z) II RING THEORY #abstractalgebra
i recommend you go to following links of total course of ring theory for complete knowledge concept and understanding so that you can perform your best in exams
playlist for complete videos of real analysis(results, theorems and questions)
https://youtube.com/playlist?list=PLabXBhS8gcsffvb7JVNWMPV_Y0XuB7msM
#ringtheory #abstractalgebra #highermaths #specialring #importantresults #proofoftheorem #bscmaths
published: 21 Nov 2020
How to Find Product/Market Fit - 3 Rings Framework
If you’re an aspiring or early-stage startup founder looking to design and launch your first (or next) big idea, consider joining my 30-day Business Model Design Challenge here:
🚀 https://runlean.ly/challenge
(Next cohort starts on Monday)
In this video, I share my 3 Rings Framework for finding Product/Market Fit systematically.
LINKS IN THE VIDEO:
📖 Check out my book Running Lean: http://runlean.ly/3e
👊 Business Model Design Challenge: https://runlean.ly/challenge
MY FREE NEWSLETTER:
📈 Free Weekly Early-stage Strategies and Tactics for Launching and Growing a Startup: https://www.leanfoundry.com/newsletter
MY OTHER SOCIALS:
🌍 My website - https://www.leanfoundry.com/
🐦 Twitter - / ashmaurya
👨💻 Linkedin - / ashmaurya
WHO AM I?
Hi - I'm Ash.
I help early-stage founder...
published: 15 Nov 2024
Rings 11 Tensor products of modules
This lecture is part of an online course on rings and modules.
We define tensor prducts of modules over more general rings, and give some examples: coproducts of commutative rings, tensors in differential geometry, tensor products of group representations, and tensor products of fields.
For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrmvrFDgwcf6XOm2TEE
published: 09 Oct 2021
Braces VS Freeze Dried Peach Rings
Braces VS Freeze Dried Peach Rings
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published: 21 Jan 2022
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published: 10 Nov 2024
Tensor products of modules over commutative rings
published: 08 Jun 2021
MediaTek's custom silicon rings in a new generation of products
With new products and smart technology use cases coming to market, MediaTek tailors its silicon to meet a variety of product needs, including the mainstream and niche product segments. Learn more about MediaTek's approach to customizable silicon, and how it specifically addresses different workloads.
Learn More:- https://i.mediatek.com/exectalk
#MediaTek #ExecTalk
Meesho rings find🥀🥀 #meesho #meesho finds #unboxing #ytshorts #shorts #random find #viral videoHey, check out this product on Meesho!
Get upto 25% OFF on your first order. Also grab extra 25% on new products every 3 hours!
https://www.meesho.com/s/p/1fc5de?utm_source=s_cc
published: 16 Nov 2024
How to Photograph Rings | Jewelry Photography Tips
We show you tips and tricks for ring photography. Similar to our product photography video, we’ll be using a tabletop setup and a combination of natural light and studio lighting.
More photography tutorials:
- Product Photography at Home: https://bhpho.to/2wWyAoV
- How to Mask in Photoshop 2020: https://bhpho.to/3kUP3i2
- Focus Stacking for Product Photography: https://bhpho.to/2weIEJX
- Macro Photography At Home: https://bhpho.to/33ZDVbl
- Studio Strobe Lighting Series https://bhpho.to/2F1uZGI
- How to Photograph Your Pets | Pet Photography Tips: https://bhpho.to/3htDWdK
Gear used:
- Nikon Z 6 Mirrorless Digital Camera with 24-70mm Lens: https://bhpho.to/2Px4Zaf
- Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED Lens: https://bhpho.to/36UtAPv
- Nikon NIKKOR Z 24-70mm f/4 S Lens: https://bh...
i recommend you go to following links of total course of ring theory for complete knowledge concept and understanding so that you can perform your best in exams...
i recommend you go to following links of total course of ring theory for complete knowledge concept and understanding so that you can perform your best in exams
playlist for complete videos of real analysis(results, theorems and questions)
https://youtube.com/playlist?list=PLabXBhS8gcsffvb7JVNWMPV_Y0XuB7msM
#ringtheory #abstractalgebra #highermaths #specialring #importantresults #proofoftheorem #bscmaths
i recommend you go to following links of total course of ring theory for complete knowledge concept and understanding so that you can perform your best in exams
playlist for complete videos of real analysis(results, theorems and questions)
https://youtube.com/playlist?list=PLabXBhS8gcsffvb7JVNWMPV_Y0XuB7msM
#ringtheory #abstractalgebra #highermaths #specialring #importantresults #proofoftheorem #bscmaths
If you’re an aspiring or early-stage startup founder looking to design and launch your first (or next) big idea, consider joining my 30-day Business Model Desig...
If you’re an aspiring or early-stage startup founder looking to design and launch your first (or next) big idea, consider joining my 30-day Business Model Design Challenge here:
🚀 https://runlean.ly/challenge
(Next cohort starts on Monday)
In this video, I share my 3 Rings Framework for finding Product/Market Fit systematically.
LINKS IN THE VIDEO:
📖 Check out my book Running Lean: http://runlean.ly/3e
👊 Business Model Design Challenge: https://runlean.ly/challenge
MY FREE NEWSLETTER:
📈 Free Weekly Early-stage Strategies and Tactics for Launching and Growing a Startup: https://www.leanfoundry.com/newsletter
MY OTHER SOCIALS:
🌍 My website - https://www.leanfoundry.com/
🐦 Twitter - / ashmaurya
👨💻 Linkedin - / ashmaurya
WHO AM I?
Hi - I'm Ash.
I help early-stage founders raise their odds of success through a battle-tested framework I’ve been curating for the past 10 years. These playbooks are taught at many of the top startup accelerators and university programs worldwide.
I’m the author of two best-selling books (Running Lean and Scaling Lean) and the creator of the popular 1-page business modeling tool Lean Canvas.
Life’s too short to build something nobody wants.
If you’re an aspiring or early-stage startup founder looking to design and launch your first (or next) big idea, consider joining my 30-day Business Model Design Challenge here:
🚀 https://runlean.ly/challenge
(Next cohort starts on Monday)
In this video, I share my 3 Rings Framework for finding Product/Market Fit systematically.
LINKS IN THE VIDEO:
📖 Check out my book Running Lean: http://runlean.ly/3e
👊 Business Model Design Challenge: https://runlean.ly/challenge
MY FREE NEWSLETTER:
📈 Free Weekly Early-stage Strategies and Tactics for Launching and Growing a Startup: https://www.leanfoundry.com/newsletter
MY OTHER SOCIALS:
🌍 My website - https://www.leanfoundry.com/
🐦 Twitter - / ashmaurya
👨💻 Linkedin - / ashmaurya
WHO AM I?
Hi - I'm Ash.
I help early-stage founders raise their odds of success through a battle-tested framework I’ve been curating for the past 10 years. These playbooks are taught at many of the top startup accelerators and university programs worldwide.
I’m the author of two best-selling books (Running Lean and Scaling Lean) and the creator of the popular 1-page business modeling tool Lean Canvas.
Life’s too short to build something nobody wants.
This lecture is part of an online course on rings and modules.
We define tensor prducts of modules over more general rings, and give some examples: coproducts ...
This lecture is part of an online course on rings and modules.
We define tensor prducts of modules over more general rings, and give some examples: coproducts of commutative rings, tensors in differential geometry, tensor products of group representations, and tensor products of fields.
For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrmvrFDgwcf6XOm2TEE
This lecture is part of an online course on rings and modules.
We define tensor prducts of modules over more general rings, and give some examples: coproducts of commutative rings, tensors in differential geometry, tensor products of group representations, and tensor products of fields.
For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrmvrFDgwcf6XOm2TEE
Braces VS Freeze Dried Peach Rings
Like for more content! :)
Get our new toothbrushes that give back here and support the Channel!! ⬇️
https://www.SomethingN...
Braces VS Freeze Dried Peach Rings
Like for more content! :)
Get our new toothbrushes that give back here and support the Channel!! ⬇️
https://www.SomethingNiceCompany.com ❤️
SUBSCRIBE AND JOIN THE FLOSSFAM 🔥🦷
Check out our other channels! @BentistReacts @Thebentistgaming
#shorts #braces #freezedried #candy #review #teeth #thebentist #dentist
Braces VS Freeze Dried Peach Rings
Like for more content! :)
Get our new toothbrushes that give back here and support the Channel!! ⬇️
https://www.SomethingNiceCompany.com ❤️
SUBSCRIBE AND JOIN THE FLOSSFAM 🔥🦷
Check out our other channels! @BentistReacts @Thebentistgaming
#shorts #braces #freezedried #candy #review #teeth #thebentist #dentist
💍✨ Sparkle up your love story without breaking the bank! 💖 Our stunning Gold Wedding Rings & Carbide Rings are now just $63.60, making it easier than ever to sa...
💍✨ Sparkle up your love story without breaking the bank! 💖 Our stunning Gold Wedding Rings & Carbide Rings are now just $63.60, making it easier than ever to say I do in style. Don't compromise on elegance or price! Grab yours today and shine like never before! 💫 #AffordableLuxury #BlissfulBargains #EngagementRing #WeddingGoals #LoveInStyle #GoldRings #CarbideRings #BudgetFriendly #FashionWithPurpose #HappilyEverAfter #lestyleparfait #lestyleparfaituk
Shop Now https://www.lestyleparfait.com/products/gold-wedding-rings-carbide-rings
💍✨ Sparkle up your love story without breaking the bank! 💖 Our stunning Gold Wedding Rings & Carbide Rings are now just $63.60, making it easier than ever to say I do in style. Don't compromise on elegance or price! Grab yours today and shine like never before! 💫 #AffordableLuxury #BlissfulBargains #EngagementRing #WeddingGoals #LoveInStyle #GoldRings #CarbideRings #BudgetFriendly #FashionWithPurpose #HappilyEverAfter #lestyleparfait #lestyleparfaituk
Shop Now https://www.lestyleparfait.com/products/gold-wedding-rings-carbide-rings
With new products and smart technology use cases coming to market, MediaTek tailors its silicon to meet a variety of product needs, including the mainstream and...
With new products and smart technology use cases coming to market, MediaTek tailors its silicon to meet a variety of product needs, including the mainstream and niche product segments. Learn more about MediaTek's approach to customizable silicon, and how it specifically addresses different workloads.
Learn More:- https://i.mediatek.com/exectalk
#MediaTek #ExecTalk
With new products and smart technology use cases coming to market, MediaTek tailors its silicon to meet a variety of product needs, including the mainstream and niche product segments. Learn more about MediaTek's approach to customizable silicon, and how it specifically addresses different workloads.
Learn More:- https://i.mediatek.com/exectalk
#MediaTek #ExecTalk
Meesho rings find🥀🥀 #meesho #meesho finds #unboxing #ytshorts #shorts #random find #viral videoHey, check out this product on Meesho!
Get upto 25% OFF on yo...
Meesho rings find🥀🥀 #meesho #meesho finds #unboxing #ytshorts #shorts #random find #viral videoHey, check out this product on Meesho!
Get upto 25% OFF on your first order. Also grab extra 25% on new products every 3 hours!
https://www.meesho.com/s/p/1fc5de?utm_source=s_cc
Meesho rings find🥀🥀 #meesho #meesho finds #unboxing #ytshorts #shorts #random find #viral videoHey, check out this product on Meesho!
Get upto 25% OFF on your first order. Also grab extra 25% on new products every 3 hours!
https://www.meesho.com/s/p/1fc5de?utm_source=s_cc
We show you tips and tricks for ring photography. Similar to our product photography video, we’ll be using a tabletop setup and a combination of natural light a...
We show you tips and tricks for ring photography. Similar to our product photography video, we’ll be using a tabletop setup and a combination of natural light and studio lighting.
More photography tutorials:
- Product Photography at Home: https://bhpho.to/2wWyAoV
- How to Mask in Photoshop 2020: https://bhpho.to/3kUP3i2
- Focus Stacking for Product Photography: https://bhpho.to/2weIEJX
- Macro Photography At Home: https://bhpho.to/33ZDVbl
- Studio Strobe Lighting Series https://bhpho.to/2F1uZGI
- How to Photograph Your Pets | Pet Photography Tips: https://bhpho.to/3htDWdK
Gear used:
- Nikon Z 6 Mirrorless Digital Camera with 24-70mm Lens: https://bhpho.to/2Px4Zaf
- Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED Lens: https://bhpho.to/36UtAPv
- Nikon NIKKOR Z 24-70mm f/4 S Lens: https://bhpho.to/2PvecQB
- Oben AT-3565 Aluminum Tripod and BZ-217T Triple-Action Ball Head: https://bhpho.to/2QLdgrX
- Profoto B10 OCF Flash Head https://bhpho.to/38uJEYg
- Profoto OCF Octa Softbox (2’): http://bhpho.to/2aH0dT9
- Profoto OCF II Filter (Rose Pink): https://bhpho.to/2XeUSvI
- Profoto OCF II Barndoors: https://bhpho.to/3bM07Z4
Shop @ B&H:
https://www.bhphotovideo.com/
Subscribe to the B&H Photo YouTube Channel
- http://bit.ly/SubscribetoBHPhoto
Follow us on Social Media
- https://www.facebook.com/bhphoto
- https://www.instagram.com/bhphoto
- https://twitter.com/BHPhotoVideo
#JewelryPhotography #ProductPhotography #PhotographyTips
We show you tips and tricks for ring photography. Similar to our product photography video, we’ll be using a tabletop setup and a combination of natural light and studio lighting.
More photography tutorials:
- Product Photography at Home: https://bhpho.to/2wWyAoV
- How to Mask in Photoshop 2020: https://bhpho.to/3kUP3i2
- Focus Stacking for Product Photography: https://bhpho.to/2weIEJX
- Macro Photography At Home: https://bhpho.to/33ZDVbl
- Studio Strobe Lighting Series https://bhpho.to/2F1uZGI
- How to Photograph Your Pets | Pet Photography Tips: https://bhpho.to/3htDWdK
Gear used:
- Nikon Z 6 Mirrorless Digital Camera with 24-70mm Lens: https://bhpho.to/2Px4Zaf
- Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED Lens: https://bhpho.to/36UtAPv
- Nikon NIKKOR Z 24-70mm f/4 S Lens: https://bhpho.to/2PvecQB
- Oben AT-3565 Aluminum Tripod and BZ-217T Triple-Action Ball Head: https://bhpho.to/2QLdgrX
- Profoto B10 OCF Flash Head https://bhpho.to/38uJEYg
- Profoto OCF Octa Softbox (2’): http://bhpho.to/2aH0dT9
- Profoto OCF II Filter (Rose Pink): https://bhpho.to/2XeUSvI
- Profoto OCF II Barndoors: https://bhpho.to/3bM07Z4
Shop @ B&H:
https://www.bhphotovideo.com/
Subscribe to the B&H Photo YouTube Channel
- http://bit.ly/SubscribetoBHPhoto
Follow us on Social Media
- https://www.facebook.com/bhphoto
- https://www.instagram.com/bhphoto
- https://twitter.com/BHPhotoVideo
#JewelryPhotography #ProductPhotography #PhotographyTips
i recommend you go to following links of total course of ring theory for complete knowledge concept and understanding so that you can perform your best in exams
playlist for complete videos of real analysis(results, theorems and questions)
https://youtube.com/playlist?list=PLabXBhS8gcsffvb7JVNWMPV_Y0XuB7msM
#ringtheory #abstractalgebra #highermaths #specialring #importantresults #proofoftheorem #bscmaths
If you’re an aspiring or early-stage startup founder looking to design and launch your first (or next) big idea, consider joining my 30-day Business Model Design Challenge here:
🚀 https://runlean.ly/challenge
(Next cohort starts on Monday)
In this video, I share my 3 Rings Framework for finding Product/Market Fit systematically.
LINKS IN THE VIDEO:
📖 Check out my book Running Lean: http://runlean.ly/3e
👊 Business Model Design Challenge: https://runlean.ly/challenge
MY FREE NEWSLETTER:
📈 Free Weekly Early-stage Strategies and Tactics for Launching and Growing a Startup: https://www.leanfoundry.com/newsletter
MY OTHER SOCIALS:
🌍 My website - https://www.leanfoundry.com/
🐦 Twitter - / ashmaurya
👨💻 Linkedin - / ashmaurya
WHO AM I?
Hi - I'm Ash.
I help early-stage founders raise their odds of success through a battle-tested framework I’ve been curating for the past 10 years. These playbooks are taught at many of the top startup accelerators and university programs worldwide.
I’m the author of two best-selling books (Running Lean and Scaling Lean) and the creator of the popular 1-page business modeling tool Lean Canvas.
Life’s too short to build something nobody wants.
This lecture is part of an online course on rings and modules.
We define tensor prducts of modules over more general rings, and give some examples: coproducts of commutative rings, tensors in differential geometry, tensor products of group representations, and tensor products of fields.
For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrmvrFDgwcf6XOm2TEE
Braces VS Freeze Dried Peach Rings
Like for more content! :)
Get our new toothbrushes that give back here and support the Channel!! ⬇️
https://www.SomethingNiceCompany.com ❤️
SUBSCRIBE AND JOIN THE FLOSSFAM 🔥🦷
Check out our other channels! @BentistReacts @Thebentistgaming
#shorts #braces #freezedried #candy #review #teeth #thebentist #dentist
💍✨ Sparkle up your love story without breaking the bank! 💖 Our stunning Gold Wedding Rings & Carbide Rings are now just $63.60, making it easier than ever to say I do in style. Don't compromise on elegance or price! Grab yours today and shine like never before! 💫 #AffordableLuxury #BlissfulBargains #EngagementRing #WeddingGoals #LoveInStyle #GoldRings #CarbideRings #BudgetFriendly #FashionWithPurpose #HappilyEverAfter #lestyleparfait #lestyleparfaituk
Shop Now https://www.lestyleparfait.com/products/gold-wedding-rings-carbide-rings
With new products and smart technology use cases coming to market, MediaTek tailors its silicon to meet a variety of product needs, including the mainstream and niche product segments. Learn more about MediaTek's approach to customizable silicon, and how it specifically addresses different workloads.
Learn More:- https://i.mediatek.com/exectalk
#MediaTek #ExecTalk
Meesho rings find🥀🥀 #meesho #meesho finds #unboxing #ytshorts #shorts #random find #viral videoHey, check out this product on Meesho!
Get upto 25% OFF on your first order. Also grab extra 25% on new products every 3 hours!
https://www.meesho.com/s/p/1fc5de?utm_source=s_cc
We show you tips and tricks for ring photography. Similar to our product photography video, we’ll be using a tabletop setup and a combination of natural light and studio lighting.
More photography tutorials:
- Product Photography at Home: https://bhpho.to/2wWyAoV
- How to Mask in Photoshop 2020: https://bhpho.to/3kUP3i2
- Focus Stacking for Product Photography: https://bhpho.to/2weIEJX
- Macro Photography At Home: https://bhpho.to/33ZDVbl
- Studio Strobe Lighting Series https://bhpho.to/2F1uZGI
- How to Photograph Your Pets | Pet Photography Tips: https://bhpho.to/3htDWdK
Gear used:
- Nikon Z 6 Mirrorless Digital Camera with 24-70mm Lens: https://bhpho.to/2Px4Zaf
- Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED Lens: https://bhpho.to/36UtAPv
- Nikon NIKKOR Z 24-70mm f/4 S Lens: https://bhpho.to/2PvecQB
- Oben AT-3565 Aluminum Tripod and BZ-217T Triple-Action Ball Head: https://bhpho.to/2QLdgrX
- Profoto B10 OCF Flash Head https://bhpho.to/38uJEYg
- Profoto OCF Octa Softbox (2’): http://bhpho.to/2aH0dT9
- Profoto OCF II Filter (Rose Pink): https://bhpho.to/2XeUSvI
- Profoto OCF II Barndoors: https://bhpho.to/3bM07Z4
Shop @ B&H:
https://www.bhphotovideo.com/
Subscribe to the B&H Photo YouTube Channel
- http://bit.ly/SubscribetoBHPhoto
Follow us on Social Media
- https://www.facebook.com/bhphoto
- https://www.instagram.com/bhphoto
- https://twitter.com/BHPhotoVideo
#JewelryPhotography #ProductPhotography #PhotographyTips
In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and Ri is a ring for every i in I, then the cartesian productΠi ∈ IRi can be turned into a ring by defining the operations coordinate-wise.
The resulting ring is called a direct product of the rings Ri. The direct product of finitely many rings coincides with the direct sum of rings.
If R = Πi ∈ IRi is a product of rings, then for every i in I we have a surjectivering homomorphismpi: R → Ri which projects the product on the ith coordinate. The product R, together with the projections pi, has the following universal property:
This shows that the product of rings is an instance of products in the sense of category theory. However, despite also being called the direct sum of rings when I is finite, the product of rings is not a coproduct in the sense of category theory. In particular, if I has more than one element, the inclusion map Ri → R is not ring homomorphism as it does not map the identity in Ri to the identity in R.
Chemists develop new process for the production of ring-shaped molecules (2023, July 6) retrieved 6 July 2023 from https.//phys.org/news/2023-07-chemists-production-ring-shaped-molecules.html.