Korean Journal of Mathematics
- Volume 13 Issue 2
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- Pages.177-182
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- 2005
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- 1976-8605(pISSN)
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- 2288-1433(eISSN)
CONGRUENCE-FREE SIMPLE SEMIGROUP
- Moon, Eunho L. (School of Liberal Arts Myongji University)
- Received : 2005.07.06
- Published : 2005.09.30
Abstract
If a semigroup S has no nontrivial congruences then S is either simple or 0-simple.([2]) By contrast with ring theory, not every congruence on a semigroup is associated with an ideal, hence some simple(or 0-simple) semigroup may have a nontrivial congruence. Thus it is a short note for the characterization of a simple(or 0-simple) semigroup that is congruence-free. A semigroup that has no nontrivial congruences is said to be congruence-free.