Ordered semigroups which are both right commutative and right cancellative
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- 作者：Niovi Kehayopulu (1) nkehayop@math.uoa.gr
Michael Tsingelis (2) mtsingelis@hol.gr - 关键词：Precongruence – ; Right commutative – ; Right cancellative – ; Left (right) ideal – ; Left simple semigroup (ordered semigroup) – ; Left zero semigroup
- 刊名：Semigroup Forum
- 出版时间：June 2012
- 出版年：2012
- 期刊代码：134_0037-1912
- 类别：mat
- 卷：84
- 期：3
- 页码：562-568
- 数据来源：sp
摘要
In this paper we prove that each right commutative, right cancellative ordered semigroup (S,.,≤) can be embedded into a right cancellative ordered semigroup (T,○,⪯) such that (T,○) is left simple and right commutative. As a consequence, an ordered semigroup S which is both right commutative and right cancellative is embedded into an ordered semigroup T which is union of pairwise disjoint abelian groups, indexed by a left zero subsemigroup of T.