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.

See also

Algebra, Arithmetic, Commutative Algebra, Discrete Mathematics, Field, Group, Group Theory, Homological Algebra, Linear Algebra, Linear Operator, Number Theory, Ring, Set Theory Explore this topic in the MathWorld classroom

Portions of this entry contributed by John Renze

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References

Ash, R. B. A Primer of Abstract Mathematics. Washington, DC: Math. Assoc. Amer., 1998.Dummit, D. S. and Foote, R. M. Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, 2004.Fraleigh, J. B. A First Course in Abstract Algebra, 7th ed. Reading, MA: Addison-Wesley, 2002.

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Abstract Algebra

Cite this as:

Weisstein, Eric W., with contributions by John Renze. "Abstract Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AbstractAlgebra.html

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