
In algebra, which is a broad division of mathematics, abstract algebra is a common name for the sub-area that studies algebraic structures in their own right. Such structures include groups, rings, fields, modules, vector spaces, and algebras. The specific term abstract algebra was coined at the beginning of the 20th century to distinguish this ar...
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http://en.wikipedia.org/wiki/Abstract_algebra

To a mathematician, real life is a special case. —anonymous Algebra that is not confined to familiar number systems, such as the real numbers, but seeks to solve equations that may involve many other kinds of system. One of its aims, in fact, is to ask: what other number systems are t...
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http://www.daviddarling.info/encyclopedia/A/abstract_algebra.html

the branch of mathematics that deals with the extension of algebraic concepts usually associated with the real number system to other, more general systems.
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https://www.infoplease.com/dictionary/abstract-algebra
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