Hostname: page-component-7dd5485656-frp75 Total loading time: 0 Render date: 2025-10-31T23:03:34.166Z Has data issue: false hasContentIssue false
  • English
  • Français

On quasi-orthodox semigroups with inverse transversals

Published online by Cambridge University Press:  20 January 2009

T. S. Blyth  and
M. H. Almeida Santos
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews, Scotland
M. H. Almeida Santos
Affiliation:
Departamento de Matemática, F.C.T., Universidade Nova de Lisboa, Portugal
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An inverse transversal of a regular semigroup S is an inverse subsemigroup So that contains precisely one inverse of each element of S. Here we consider the case where S is quasi-orthodox. We give natural characterisations of such semigroups and consider various properties of congruences.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 505 - 514
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

REFERENCES

1.Blyth, T. S. and Santos, M. H. Almeida, A simplistic approach to inverse transversals, Proc. Edinburgh Math. Soc. 39 (1996), 57–69.CrossRefGoogle Scholar
2.Blyth, T. S. and Santos, M. H. Almeida, Congruences associated with inverse transversals, Collectanea Mathematica, memorial volume for Paul Dubreil, 46 (1995), 35–48.Google Scholar
3.Hall, T. E., Congruences and Green's relations on regular semigroups, Glasgow Math. J. 13 (1972), 167–175.CrossRefGoogle Scholar
4.Mcalister, D. B. and Mcfadden, R., Semigroups with inverse transversals as matrix semigroups, Quart. J. Math. Oxford 25 (1984), 455–474.CrossRefGoogle Scholar
5.Saito, Tatsuhiko, Construction of regular semigroups with inverse transversals, Proc. Edinburgh Math. Soc. 32 (1989), 41–51.CrossRefGoogle Scholar
6.Saito, Tatsuhiko, Quasi-orthodox semigroups with inverse transversals, Semigroups Forum 36 (1987), 47–54.CrossRefGoogle Scholar
7.Tang, Xilin, Regular semigroups with inverse transversals, preprint.Google Scholar
8.Yamada, M., Structure of quasi-orthodox semigroups, Mem. Fac. Sc, Shimane Univ. 14 (1980), 1–18.Google Scholar