List of abstract algebra topics


List of abstract algebra topics

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called elementary algebra. The distinction is rarely made in more recent writings.

Contents

Overview

History

Basic language

Semigroups and monoids

Group theory

Ring theory

Field theory

Module theory

Representation theory

Representation theory

Non-associative systems

Generalities

Computer algebra

See also


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