Ring theory

Glossary of ring theory

Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. For the items in commutative algebra (the theory of commutative rings), see glossary of commutative algebra. For ring-theoretic concepts in the language of modules, see also Glossary of module theory. For specific types of algebras, see also: Glossary of field theory and Glossary of Lie groups and Lie algebras. Since, currently, there is no glossary on not-necessarily-associative algebra-structures in general, this glossary includes some concepts that do not need associativity; e.g., a derivation. (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

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Abstract Algebra: The definition of a Ring

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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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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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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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From playlist A Short Course in Algebra and Number Theory

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From playlist OWASP AppSec USA 2010

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Algebraic number theory and rings I | Math History | NJ Wildberger

In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. In this way the notion of an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include

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Introduction to number theory lecture 29. Rings in number theory

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My favorite LaTeX packages for writing beautiful math documents

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From playlist LaTeX Tutorials

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Abstract Algebra | What is a ring?

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From playlist Abstract Algebra

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