Maximal cancellative subsemigroups and cancellative congruences
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- by Mohan S. Putcha PDF
- Proc. Amer. Math. Soc. 47 (1975), 49-52 Request permission
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 $S$.References
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- Takayuki Tamura, ${\cal N}$-congruences of ${\cal N}$-semigroups, J. Algebra 27 (1973), 11–30. MR 327956, DOI 10.1016/0021-8693(73)90162-2
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 49-52
- DOI: https://doi.org/10.1090/S0002-9939-1975-0352308-1
- MathSciNet review: 0352308