Invariant semigroups of orthodox semigroups

T. S. Blyth; M. H. Almeida-Santos

doi:10.1007/BF02574093

Invariant semigroups of orthodox semigroups

T. S. Blyth, M. H. Almeida-Santos

DM - Departamento de Matemática

Research output: Contribution to journal › Article › peer-review

Abstract

We consider, in a right inverse semigroup S with a multiplicative inverse transversal S^o, the notion of an S^o-invariant subsemigroup and use this to describe all the left amenable orders definable on S. The results obtained, together with their duals, are used to prove that if S is an orthodox semigroup with a multiplicative inverse transversal S^o, then every amenable order on S^o can be extended to a unique amenable order on S.

Original language	English
Pages (from-to)	163-180
Number of pages	18
Journal	Semigroup Forum
Volume	52
Issue number	1
DOIs	https://doi.org/10.1007/BF02574093
Publication status	Published - 1 Dec 1996

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N2 - We consider, in a right inverse semigroup S with a multiplicative inverse transversal So, the notion of an So-invariant subsemigroup and use this to describe all the left amenable orders definable on S. The results obtained, together with their duals, are used to prove that if S is an orthodox semigroup with a multiplicative inverse transversal So, then every amenable order on So can be extended to a unique amenable order on S.

AB - We consider, in a right inverse semigroup S with a multiplicative inverse transversal So, the notion of an So-invariant subsemigroup and use this to describe all the left amenable orders definable on S. The results obtained, together with their duals, are used to prove that if S is an orthodox semigroup with a multiplicative inverse transversal So, then every amenable order on So can be extended to a unique amenable order on S.

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Invariant semigroups of orthodox semigroups

Abstract

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