Ring theory | Categories in category theory

Category of rings

In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that preserve the identity). Like many categories in mathematics, the category of rings is large, meaning that the class of all rings is proper. (Wikipedia).

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RNT1.1. Definition of Ring

Ring Theory: We define rings and give many examples. Items under consideration include commutativity and multiplicative inverses. Example include modular integers, square matrices, polynomial rings, quaternions, and adjoins of algebraic and transcendental numbers.

From playlist Abstract 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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Rings and modules 2: Group rings

This lecture is part of an online course on rings and modules. We decribe some examples of rings constructed from groups and monoids, such as group rings and rings of Dirichlet polynomials. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrm

From playlist Rings and modules

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Abstract Algebra 2.1: Introduction to Rings

In this video, I will introduce rings and basic examples of rings. Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=jesyk7_ti6Q Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika Email : fematikaqna

From playlist Abstract Algebra

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Visual Group Theory, Lecture 7.1: Basic ring theory

Visual Group Theory, Lecture 7.1: Basic ring theory A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties.

From playlist Visual Group Theory

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Rings and modules 1 Introduction

This lecture is part of an online course on ring theory, at about the level of a first year graduate course or honors undergraduate course. This is the introductory lecture, where we recall some basic definitions and examples, and describe the analogy between groups and rings. For the

From playlist Rings and modules

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RNT1.4. Ideals and Quotient Rings

Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.

From playlist Abstract Algebra

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Magic Rings

11 rings form a ball.

From playlist Handmade geometric toys

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Abstract Algebra | Types of rings.

We define several and give examples of different types of rings which have additional structure. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Paul-André Melliès - A Functorial Excursion between Algebraic Geometry and Linear Logic

In this talk, I will use the functor of points approach to Algebraic Geometry to establish that every covariant presheaf X on the category of commutative rings — and in particular every scheme X — comes equipped “above it” with a symmetric monoidal closed category PshModX of presheaves of

From playlist Combinatorics and Arithmetic for Physics: special days

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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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Localization of Rings as Localizations of Categories

We show what it means to localize a category at a set of morphisms and show that usual localization of rings is an instance of this definition.

From playlist Category Theory

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Representations on KU-modules - David Treumann

Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Representations on KU-modules Speaker: David Treumann Affiliation: Boston College Date: November 18, 2020 For more video please visit http://video.ias.edu

From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory

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Lecture 9: Properties of THH

In this video, we prove certain formal properties of THH, for example that it has a universal property in the setting of commutative rings. We also show base-change properties and use these to compute THH of perfect rings. Feel free to post comments and questions at our public forum at h

From playlist Topological Cyclic Homology

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Duality in Higher Categories-I 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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Arthur-César Le Bras - Prismatic Dieudonné theory

Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo du 22 avril 2020 I would like to explain a classification result for p-divisible groups, which unifies many of the existing results in the literature. The main tool is the theory of prisms and prismatic cohomology recently developed by

From playlist Conférences Paris Pékin Tokyo

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Rings and midules 3: Burnside ring and rings of differential operators

This lecture is part of an online course on rings and modules. We discuss a few assorted examples of rings. The Burnside ring of a group is a ring constructed form the permutation representations. The ring of differentail operators is a ring whose modules are related to differential equat

From playlist Rings and modules

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Complete category | Category of sets | Quotient ring | Integral domain | Category of abelian groups | Finite field | Subring | Zero ring | Ideal (ring theory) | Free product | Free object | Coproduct | Reflective subcategory | Free product of associative algebras | Group (mathematics) | Isomorphism | Commutative algebra | Monoid (category theory) | Forgetful functor | Pullback (category theory) | Symmetric monoidal category | Congruence relation | Principal ideal domain | Rng (algebra) | Preadditive category | Categories for the Working Mathematician | Product (category theory) | Polynomial ring | Algebra (ring theory) | Matrix ring | Monoid | Injective object | Field extension | Category of affine schemes | Monoid ring | Connected category | Characteristic (algebra) | Mathematics | Coequalizer | Field (mathematics) | Function (mathematics) | Integer | Equivalence of categories | Ring homomorphism | Set (mathematics) | Isomorphism of categories | Cartesian product | Ring (mathematics) | Zero morphism | Projective line over a ring | Category (mathematics) | Morphism | Concrete category | Monomorphism | Prime number | Scheme (mathematics) | Subcategory | Class (set theory) | Category of groups | Epimorphism | Spectrum of a ring | Opposite category | Abelian group | Module (mathematics) | Commutative ring