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{{r|abstract algebra}}

...umber]]s and later to arbitrary [[field]]s. In the second place notions of abstract algebra have led to a natural generalization of algebraic geometry, namely to the c

{{r|Abstract algebra}}

...mials, we need only know how to add and multiply their coefficients. In [[abstract algebra]], an abstract collection of objects that can be added and multiplied subje ...number'' when one thinks of a function. The distinction is important in [[abstract algebra]], because what we have called "constant numbers" is more generally replace

In [[abstract algebra]], '''pointwise operation''' is a way of extending an [[operation (mathemat

In [[abstract algebra]], the '''group isomorphism problem''' is the [[decision problem]] of deter

In [[abstract algebra]], a linear map is a [[homomorphism]] of vector spaces.

In [[mathematics]], particularly in [[abstract algebra]] and [[homological algebra]], an '''exact sequence''' is a sequence of alg

The term '''basis''' is also used in [[abstract algebra]], specifically in the theory of [[free module]]s. For more on this use of

In the [[mathematics|mathematical]] field of [[abstract algebra]], an '''abelian group''' is a type of [[group (mathematics)|group]] in whi

* '''[[Abstract algebra]]''', sometimes also called ''modern algebra'', in which [[algebraic struct == Abstract algebra ==

...hematical physics]]. This article deals exclusively with fields as used in abstract algebra.

...hin pure mathematics, modular arithmetic is of fundamental importance in [[abstract algebra]] and [[number theory]].

In 1870, he introduced a major contribution to the development of modern abstract algebra, his ''[[Linear Associative Algebra]]''.<ref>Helena M. Pycior, "Benjamin Pe

...his books, in particular ''Algebra'', his graduate-level introduction to [[abstract algebra]]. Lang's ''Algebra'', a graduate-level introduction to [[abstract algebra]], was a highly influential text that ran through numerous updated editions

...nd [[vector space]]s are particular types. They have become ubiquitous in abstract algebra and other areas of mathematics that involve algebraic structures, such as a

* 1832: Galois theory is developed by [[Évariste Galois]] in his work on abstract algebra.<ref name="Stewart"> </ref>

...ples, is that of the abstract [[ring (mathematics)|ring]] encountered in [[abstract algebra]].

[[Abstract algebra]] studies abstract number systems such as [[group (mathematics)|group]]s, [

In [[abstract algebra]], we get some related structures which are similar to groups by relaxing s * Herstein, I.N. ''Abstract Algebra'', Wiley, ISBN 0-471-36879-2