Commutative semigroups whose homomorphic images in groups are groups |
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Authors: | Mohan S. Putcha |
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Affiliation: | (1) Department of Mathematics, University of California, Santa Barbara, 93106 Santa Barbara, California |
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Abstract: | In this paper we study commutative semigroups whose every homomorphic image in a group is a group. We find that for a commutative semigroup S, this property is equivalent to S being a union of subsemigroups each of which either has a kernel or else is isomorphic to one of a sequence T0, T1, T2, ... of explicitly given, countably infinite semigroups without idempotents. Moreover, if S is also finitely generated then this property is equivalent to S having a kernel. |
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