abstract algebra

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The area of mathematics concerned with algebraic structures, such as groups, rings and fields, involving sets of elements with particular operations satisfying certain axioms. The purpose is to derive, from the set of axioms, general results that are then applicable to any particular example of the algebraic structure in question. The theory of certain algebraic structures is highly developed; in particular, the theory of vector spaces is so extensive that its study, known as linear algebra, would probably no longer be classified as abstract algebra.

Subjects: Mathematics.

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