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 ,
Ring ,
Set Theory Explore this topic in the MathWorld classroom
Portions of this entry contributed by John
Renze
Explore with Wolfram|Alpha
References Ash, R. B. A Primer of Abstract Mathematics. Dummit,
D. S. and Foote, R. M. Abstract
Algebra, 2nd ed. Fraleigh,
J. B. A
First Course in Abstract Algebra, 7th ed. Referenced
on Wolfram|Alpha Abstract Algebra
Cite this as:
Renze, John and Weisstein, Eric W. "Abstract Algebra." From MathWorld https://mathworld.wolfram.com/AbstractAlgebra.html
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