Commutative algebra | Algebraic structures | Ring theory

Simplicial commutative ring

In algebra, a simplicial commutative ring is a commutative monoid in the category of simplicial abelian groups, or, equivalently, a simplicial object in the category of commutative rings. If A is a simplicial commutative ring, then it can be shown that is a ring and are modules over that ring (in fact, is a graded ring over .) A topology-counterpart of this notion is a commutative ring spectrum. (Wikipedia).

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Commutative algebra 2 (Rings, ideals, modules)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. This lecture is a review of rings, ideals, and modules, where we give a few examples of non-commutative rings and rings without

From playlist Commutative algebra

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Commutative algebra 1 (Introduction)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. https://link.springer.com/book/10.1007/978-1-4612-5350-1 This is a short introductory lecture, and gives a few examples of the

From playlist Commutative algebra

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Commutative algebra 53: Dimension Introductory survey

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give an introductory survey of many different ways of defining dimension. Reading: Section Exercises:

From playlist Commutative algebra

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Commutative algebra 9 (Euclidean domains)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We describe one method of visualizing rings by drawing pictures of their points, and use this to show that the ring of Gaussia

From playlist Commutative algebra

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Definition of a Ring and Examples of Rings

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Ring and Examples of Rings - Definition of a Ring. - Definition of a commutative ring and a ring with identity. - Examples of Rings include: Z, Q, R, C under regular addition and multiplication The Ring of all n x

From playlist Abstract Algebra

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Commutative algebra 19 Affine schemes

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we give an introduction to the affine scheme of a ring, that is heavily used in algebraic geometry. We check t

From playlist Commutative algebra

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Every Boolean Ring is Commutative Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Every Boolean Ring is Commutative Proof

From playlist Abstract Algebra

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A Ring is Commutative iff (a - b)(a + b) = a^2 - b^2 Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A Ring is Commutative iff (a - b)(a + b) = a^2 - b^2 Proof. A proof that (a - b)(a + b) = a^2 - b^2 for all a, b in R if and only if R is a commutative ring.

From playlist Abstract Algebra

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Lecture 6: HKR and the cotangent complex

In this video, we discuss the cotangent complex and give a proof of the HKR theorem (in its affine version) Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-m

From playlist Topological Cyclic Homology

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Lecture 3: Classical Hochschild Homology

In this video, we introduce classical Hochschild homology and discuss the HKR theorem. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-muenster.de/IVV5WS/Web

From playlist Topological Cyclic Homology

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Lecture 7: Hochschild homology in ∞-categories

In this video, we construct Hochschild homology in an arbitrary symmetric-monoidal ∞-category. The most important special case is the ∞-category of spectra, in which we get Topological Hochschild homology. Feel free to post comments and questions at our public forum at https://www.uni-mu

From playlist Topological Cyclic Homology

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Commutative algebra 61: Examples of regular local rings

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give some examples of regular local rings. We first give an example of a regular local ring that is not geometrically regul

From playlist Commutative algebra

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Kęstutis Česnavičius - Purity for Flat Cohomology

The absolute cohomological purity conjecture of Grothendieck proved by Gabber ensures that on regular schemes étale cohomology classes of fixed cohomological degree extend uniquely over closed subschemes of large codimension. I will discuss the corresponding phenomenon for flat cohomology.

From playlist Journée Gretchen & Barry Mazur

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Duality In Higher Categories II by Pranav Pandit

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

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Noether's works in Topology by Indranil Biswas

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

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Minimal Models by Somnath Basu

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

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Charles Rezk: Elliptic cohomology and elliptic curves (Part 3)

The lecture was held within the framework of the Felix Klein Lectures at Hausdorff Center for Mathematics on the 8. June 2015

From playlist HIM Lectures 2015

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Stable Homotopy Seminar, 14: The stable infinity-category of spectra

I give a brief introduction to infinity-categories, including their models as simplicially enriched categories and as quasi-categories, and some categorical constructions that also make sense for infinity-categories. I then describe what it means for an infinity-category to be stable and h

From playlist Stable Homotopy Seminar

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Yonatan Harpaz - New perspectives in hermitian K-theory III

For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu

From playlist New perspectives on K- and L-theory

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5B Commutative Law of Matrix Multiplication-YouTube sharing.mov

A closer look at three examples of the Commutative Law of Matrix Multiplication.

From playlist Linear Algebra

Related pages

Commutative ring spectrum | Derived scheme | Module (mathematics) | Chain complex | Graded ring | Topology | Algebra | Opposite category | Dold–Kan correspondence | Module spectrum | Category (mathematics) | Polynomial differential form | Commutative ring