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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Maximal cancellative subsemigroups and cancellative congruences


Author: Mohan S. Putcha
Journal: Proc. Amer. Math. Soc. 47 (1975), 49-52
MathSciNet review: 0352308
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Abstract: A subsemigroup $ T$ of a commutative semigroup $ S$ is called a mild ideal if for any $ a \in S,aT \cap T \ne \phi $. It is shown here that any maximal cancellative subsemigroup $ T$ of a commutative, idempotent-free, archimedean semigroup $ S$ must be a mild ideal of $ S$. Maximal cancellative subsemigroups exist in abundance due to Zorn's lemma. It is also shown that if $ T$ is mild ideal of a commutative semigroup $ S$, then every cancellative congruence of $ T$ has a unique extension to a cancellative congruence of $ S$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0352308-1
PII: S 0002-9939(1975)0352308-1
Keywords: Semigroups, commutative, archimedean, maximal cancellative congruence, mild ideal
Article copyright: © Copyright 1975 American Mathematical Society