Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-12T05:49:39.839Z Has data issue: false hasContentIssue false
  • English
  • Français

Extensions of regular orthogroups by groups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Mária B. Szendrei
Mária B. Szendrei
Affiliation:
József Attila University, Bolyai Institute, 6720 Szeged, Aradi vértanúk tere 1, Hungary, email: M.Szendrei@math.u-szeged.hu
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.

A common generalization of the author's embedding theorem concerning the E-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented. We prove that each orthodox semigroup with a regular band of idempotents, which is an extension of an orthogroup K by a group, can be embedded into a semidirect product of an orthogroup K′ by a group, where K′ belongs to the variety of orthogroups generated by K. The proof is based on a criterion of embeddability into a semidirect product of an orthodox semigroup by a group and uses bilocality of orthogroup bivarieties.

MSC classification

Secondary: 20M10: General structure theory 20M19: Orthodox semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 28 - 60
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Billhardt, B., ‘On inverse semigroups the closure of whose set of idempotents is a Clifford semigroup’, Semigroup Forum 44 (1992), 320–331.Google Scholar
[2]Howie, J. M., An introduction to semigroup theory (Academic Press, London, 1976).Google Scholar
[3]Ismaeel, A. A., ‘An embedding of Eω-Clifford semigroups’, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 37 (1994), 29–39.Google Scholar
[4]Kaďourek, J. and Szendrei, M. B., ‘A new approach in the theory of orthodox semigroups’, Semigroup Forum 40 (1990), 257–296.CrossRefGoogle Scholar
[5]McAlister, D. B., ‘Groups, semilattices and inverse semigroups II’, Trans. Amer. Math. Soc. 196 (1974), 351–370.CrossRefGoogle Scholar
[6]O'Carroll, L., ‘Embedding theorems for proper inverse semigroups’, J. Algebra 42 (1976), 26–40.Google Scholar
[7]Szendrei, M. B., ‘E-unitary regular semigroups’, Proc. Roy. Soc. Edinburgh Sect. A 106 (1987), 89–102.Google Scholar
[8]Szendrei, M. B., ‘Orthogroup bivarieties are bilocal’, in: Semigroups with applications, Proceedings of the Conference Oberwolfach 21–28 07 1991 (World Scientific, Singapore, 1992), pp. 114–131.Google Scholar
[9]Szendrei, M. B., ‘On embeddability into a semidirect product of an orthodox semigroup by a group’, Acta Sci. Math.(Szeged) 57 (1993), 601–612.Google Scholar
[10]Tilson, B., ‘Categories as algebra: an essential ingredient in the theory of monoids’, J. Pure Appl. Algebra 48 (1987), 83–198.Google Scholar
[11]Venkatesan, P. S., ‘Right (left) inverse semigroups,’ J. Algebra 31 (1974), 209–217.CrossRefGoogle Scholar
[12]Yamada, M., ‘Orthodox semigroups whose idempotents satisfy a certain identity’, Semigroup Forum, 6 (1973), 113–128.Google Scholar