Hostname: page-component-7857688df4-8r446 Total loading time: 0 Render date: 2025-11-18T04:43:11.088Z Has data issue: false hasContentIssue false
  • English
  • Français

On left quasinormal orthodox semigroups

Published online by Cambridge University Press:  14 November 2011

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

Synopsis

The existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroup S is locally inverse and orthodox if and only if there exists a local isomorphism from S onto an inverse semigroup T.

In this paper, we show the existence of a smallest R-unipotent congruence ρ on an orthodox semigroup S and give its expression in the case where S is also left quasinormal. Finally, we prove that a regular semigroup S is left quasinormal and orthodox if and only if there exists a local isomorphism from S onto an R-unipotent semigroup T.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 59 - 71
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.)

Article purchase

Temporarily unavailable

References

1Blyth, T. S. and Gomes, Gracinda M. S.. On the compatibility of the natural order on a regular semigroup. Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 79–84.CrossRefGoogle Scholar
2Edwards, Constance C.. The greatest idempotent separating congruence on an L-unipotent semigroup. Semigroup Forum 14 (1977), 127–135.CrossRefGoogle Scholar
3Edwards, Constance C.. The minimum group congruence on an L-unipotent semigroup. Semigroup Forum 18 (1979), 9–14.Google Scholar
4Hall, T. E.. On regular semigroups whose idempotents form a subsemigroup. Bull. Austral. Math. Soc. 1 (1969), 195–208.CrossRefGoogle Scholar
5Howie, J. M.. An introduction to Semigroup Theory (London: Academic Press, 1976).Google Scholar
6Howie, J. M. and Lallement, G.. Certain fundamental congruences on a regular semigroup. Proc. Glasgow Math. Assoc. 7 (1966), 145–159.CrossRefGoogle Scholar
7McAlister, D. B.. Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups. J. Austral. Math. Soc. (Series A) 31 (1981), 325–336.CrossRefGoogle Scholar
8McAlister, D. B.. Rees matrix covers for locally inverse semigroups, (to appear).Google Scholar
9Meakin, J. C.. Congruences on orthodox semigroups. J. Austral. Math. Soc. 12 (1971), 323–341.CrossRefGoogle Scholar
10Meakin, J. C.. Congruences on orthodox semigroups II. J. Austral. Math. Soc. 13 (1972), 259–266.CrossRefGoogle Scholar
11Meakin, J. C.. The Rees construction in regular semigroups. (Submitted).Google Scholar
12Meakin, J. C. and Nambooripad, K. S. S.. Coextensions of regular semigroups by rectangular bands I. Trans. Amer. Math. Soc. 269 (1982), 197–224.Google Scholar
13Nambooripad, K. S. S.. The natural partial order on a regular semigroup. Proc. Edinburgh Math. Soc. 23 (1980), 249–260.Google Scholar
14Petrich, M.. Lectures in Semigroups (Berlin: Akademic Verlag, 1977).Google Scholar
15Venkatesan, P. S.. Right (left) inverse semigroups. J. Algebra 31 (1974), 209–217.CrossRefGoogle Scholar
16Venkatesan, P. S.. On right unipotent semigroups. Pacific J. Math. 63 (1976), 555–561.CrossRefGoogle Scholar
17Yamada, M.. Regular semigroups whose idempotents satisfy permutation identities. Pacific J. Math. 21 (1967), 371–392.CrossRefGoogle Scholar
18Yamada, M.. On a regular semigroup in which the idempotents form a band. Pacific J. Math. 33 (1970), 261–272.Google Scholar