CBSE Class 12-science Answered

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 (1998) 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.