order definition in modern
algebra
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It is the smallest positive integer m such that am = e, where e denotes the identity element of the group, and am denotes the product of m copies of a. If no such m exists, a is said to have infinite order.
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In algebra, which is a broad division of mathematics, abstract algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras.
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