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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Conditions for commutative semigroups to have nontrivial homomorphisms into nonnegative (positive) reals


Author: Yuji Kobayashi
Journal: Proc. Amer. Math. Soc. 65 (1977), 199-203
MSC: Primary 20M15
DOI: https://doi.org/10.1090/S0002-9939-1977-0447450-2
MathSciNet review: 0447450
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Abstract: Let S be a commutative cancellative semigroup of finite rank (the free rank of the quotient group of S is finite). We give a necessary and sufficient condition for S to have a nontrivial homomorphism into the additive semigroup of nonnegative (positive) reals. We also give a counter-example in the case of infinite rank.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0447450-2
Keywords: Commutative cancellative semigroup, quotient group, rank, convex cone
Article copyright: © Copyright 1977 American Mathematical Society