Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-27T22:54:19.255Z Has data issue: false hasContentIssue false
  • English
  • Français

Regular semigroups with a multiplicative inverse transversal

Published online by Cambridge University Press:  14 November 2011

T. S. Blyth  and
R. McFadden
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews
R. McFadden
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

By an inverse transversal of a regular semigroup S we mean an inverse subsemigroup that contains a single inverse of every element of S. A certain multiplicative property (which in the case of a band is equivalent to normality) is imposed on an inverse transversal and a complete description of the structure of S is obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 253 - 270
Copyright
Copyright © Royal Society of Edinburgh 1982

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

1Blyth, T. S. and R. McFadden. On the construction of a class of regular semigroups. J. Algebra (to appear).Google Scholar
2Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups, volumes I and II. Math. Surveys of the Amer. Math. Soc. 7 (Providence, R.I., 1961, 1967).Google Scholar
3Edwards, C. C.. The greatest idempotent separating congruence on an ℒ-unipotent semigroup. Semigroup Forum 14 (1977), 127–135.CrossRefGoogle 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
6McAlister, D. B.. Regular Rees matrix semigroups and regular Dubreil-Jacobin semigroups. J. Austral. Math. Soc. Ser. A 31 (1981), 325–336.CrossRefGoogle Scholar
7McAlister, D. B. and Blyth, T. S.. Split orthodox semigroups. J. Algebra 51 (1978), 491–525.CrossRefGoogle Scholar
8Nambooripad, K. S. S.. Structure of regular semigroups I. Mem. Amer. Math. Soc. 22 (224), (1979).Google Scholar
9Yamada, M. and Kimura, N.. Note on idempotent semigroups II. Proc. Japan Acad. 34 (1958), 110–112.Google Scholar