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

Arithmetic,

Algebra,

Commutative Algebra,

Discrete
Mathematics,

Field,

Group,

Group Theory,

Homological
Algebra,

Linear Algebra,

Linear
Operator,

Number Theory,

Representation
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, 2nd ed.* Englewood Cliffs, NJ: Prentice-Hall, 1998.Fraleigh,
J. B. *A
First Course in Abstract Algebra, 7th ed.* Reading, MA: Addison-Wesley, 2002.## Referenced
on Wolfram|Alpha

Abstract Algebra
## Cite this as:

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

## Subject classifications