Ring Definition

Course:
Abstract Algebra

A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a ring.

A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a ring.

Lessons
Course Info
What is Abstract Algebra?
Group Definition
Group Definition (Quick)
Cosets and Lagrange's Theorem
Cayley Tables
Groups - Motivation for Definition
Normal Subgroups and Factor Groups
Subgroups
Cyclic Groups
Group or Not Group? (Integer Edition)
Group Homomorphisms
Group Homomorphisms (Quick)
Isomorphisms for Groups
Kernel of Group Homomorphisms
Order of an Element
Cycle Notation for Permutations
Symmetric Groups
Dihedral Groups
Direct Products of Groups
Matrix Groups
Simple Groups
Symmetry Groups of Triangles
Ring Definition
Ring Definition (Quick)
Ring Examples
Units in a Ring
Field Definition
Field Definition (Quick)
Field Examples: Infinite Fields
Ideals in Rings
Integral Domains
Modules
Vector Spaces
Course Page
Abstract Algebra
Course Description
Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.