Hostname: page-component-6bf8c574d5-mggfc Total loading time: 0 Render date: 2025-02-21T13:47:37.382Z Has data issue: false hasContentIssue false
  • English
  • Français

On the compatibility of the natural order on a regular semigroup

Published online by Cambridge University Press:  14 November 2011

T. S. Blyth  and
Gracinda M. S. Gomes
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews
Gracinda M. S. Gomes
Affiliation:
Mathematical Institute, University of St Andrews
Get access Rights & Permissions [Opens in a new window]

Synopsis

A notable achievement in the algebraic theory of semigroups has been the discovery by Nambooripad of the natural order on a regular semigroup. He has shown that this order is compatible with multiplication if and only if the semigroup is locally inverse, in the sense that every local submonoid is an inverse semigroup. In this paper we determine precisely when the natural order is compatible on the right (respectively left) with multiplication; this is so if and only if every local submonoid is ℒ-unipotent (respectively ℛ-unipotent).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 79 - 84
Copyright
Copyright © Royal Society of Edinburgh 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Edwards, C. C.. The greatest idempotent-separating congruence on an ℒ-unipotent semigroup, Semigroup Forum 14 (1977), 127–135.CrossRefGoogle Scholar
2McAlister, D. B.. Rees matrix covers for locally inverse semigroups (to appear).Google Scholar
3Nambooripad, K. S. S.. The structure of regular semigroups I. Mem. Amer. Math. Soc. 22, No. 224 (1979).Google Scholar
4Nambooripad, K. S. S.. The natural partial order on a regular semigroup. Proc. Edinburgh Math. Soc. 23 (1980), 249–260.Google Scholar
5Petrich, M.. Lectures in Semigroups (New York: Wiley, 1977).Google Scholar