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Abstract Algebra

Basic definition

Abstract algebra is the set of advanced topics in algebra that deal with abstract algebraic structures rather than the usual number systems.

Detailed definition

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields. Important branches of abstract algebra are commutative algebra, representation theory, and homological algebra. Linear algebra, elementary number theory, and discrete mathematics are sometimes considered branches of abstract algebra. Ash includes the following areas in his definition of abstract algebra: logic and foundations, counting, elementary number theory, informal set theory, linear algebra, and the theory of linear operators.

Related terms

algebra | arithmetic | commutative algebra | discrete mathematics | field | group | group theory | homological algebra | linear algebra | linear operator | number theory | ring | set theory

Educational grade level

college level

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