Orders and straight left orders in completely regular semigroups

Victoria Gould; Paula Smith

Orders and straight left orders in completely regular semigroups

Mathematics

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

Abstract

A subsemigroup S of a completely regular semigroup Q is an order in Q if every element of Q can be written as a(#)b and as cd(#) where a, b, c,d is an element of S and x(#) is the inverse of x is an element of Q in ri subgroup of e. If only the first condition holds and one insists also that a R b in e, then S is said to be a straight left order in e. This paper characterizes those semigroups that are straight left orders in completely regular semigroups. A consequence of this result, together with some technicalities concerning lifting of morphisms, is a description of orders in completely regular semigroups. 2000 Mathematics Subject Classification: 20 M 10.

Original language	English
Pages (from-to)	193-214
Number of pages	22
Journal	Monatshefte fur Mathematik
Volume	131
Issue number	3
Publication status	Published - 2000

Keywords

group inverse
order
completely regular
QUOTIENTS

Cite this

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AU - Smith, Paula

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N2 - A subsemigroup S of a completely regular semigroup Q is an order in Q if every element of Q can be written as a(#)b and as cd(#) where a, b, c,d is an element of S and x(#) is the inverse of x is an element of Q in ri subgroup of e. If only the first condition holds and one insists also that a R b in e, then S is said to be a straight left order in e. This paper characterizes those semigroups that are straight left orders in completely regular semigroups. A consequence of this result, together with some technicalities concerning lifting of morphisms, is a description of orders in completely regular semigroups. 2000 Mathematics Subject Classification: 20 M 10.

AB - A subsemigroup S of a completely regular semigroup Q is an order in Q if every element of Q can be written as a(#)b and as cd(#) where a, b, c,d is an element of S and x(#) is the inverse of x is an element of Q in ri subgroup of e. If only the first condition holds and one insists also that a R b in e, then S is said to be a straight left order in e. This paper characterizes those semigroups that are straight left orders in completely regular semigroups. A consequence of this result, together with some technicalities concerning lifting of morphisms, is a description of orders in completely regular semigroups. 2000 Mathematics Subject Classification: 20 M 10.

KW - group inverse

KW - order

KW - completely regular

KW - QUOTIENTS

M3 - Article

VL - 131

SP - 193

EP - 214

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 3

ER -