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Arithmetic and Ideal Theory of Commutative Semigroups
Annals of Mathematics, 1938A set S in which a multiplication ab is defined is called a semigroup if this multiplication is associative and commutative, if an identity element is present in S, and if the cancellation law holds: ab = ac implies b = c. For example, the non-zero elements of a domain of integrity constitute a semigroup under multiplication.
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