Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T15:16:01.902Z Has data issue: false hasContentIssue false
  • English
  • Français

A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS

Part of: Semigroups

Published online by Cambridge University Press:  01 April 2009

XIANGJUN KONG  and
XIANZHONG ZHAO
XIANGJUN KONG*
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, People’s Republic of China
XIANZHONG ZHAO
Affiliation:
Department of Mathematics, Northwest University, Xi’an, Shaanxi 710069, People’s Republic of China
*
✉For correspondence; e-mail: xiangjunkong97@163.com
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.

In any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.

Keywords

regular semigroupinverse transversalorthodox transversalquasi-ideal

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 177 - 187
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Blyth, T. S. and Almeida Santos, M. H., ‘A classification of inverse transversal’, Comm. Algebra 29(2) (2001), 611–624.Google Scholar
[2]Blyth, T. S. and Almeida Santos, M. H., ‘Amenable orders associated with inverse transversals’, J. Algebra 240(1) (2001), 143–164.Google Scholar
[3]Blyth, T. S. and McFadden, R. B., ‘Regular semigroups with a multiplicative inverse transversal’, Proc. Roy. Soc. Edinburgh A 92 (1982), 253–270.Google Scholar
[4]Chen, J., ‘On regular semigroups with orthodox transversals’, Comm. Algebra 27 (1999), 4275–4288.Google Scholar
[5]Chen, J. and Guo, Y., ‘Orthodox transversals of regular semigroups’, Internat. J. Algebra Comput. 11(2) (2001), 269–279.Google Scholar
[6]Howie, J. M., An Introduction to Semigroup Theory (Academic Press, London, 1976).Google Scholar
[7]Kong, X., ‘Regular semigroups with quasi-ideal orthodox transversals’, Semigroup Forum 74 (2007), 247–258.Google Scholar
[8]McAlister, D. B. and McFadden, R. B., ‘Regular semigroups with inverse transversals’, Q. J. Math. 34(2) (1983), 459–474.CrossRefGoogle Scholar
[9]Saito, T., ‘Structure of regular semigroups with a quasi-ideal inverse transversal’, Semigroup Forum 31 (1985), 305–309.CrossRefGoogle Scholar
[10]Saito, T., ‘A note on regular semigroups with inverse transversals’, Semigroup Forum 33 (1986), 149–152.CrossRefGoogle Scholar
[11]Tang, X., ‘Regular semigroups with inverse transversals’, Semigroup Forum 55 (1997), 25–32.Google Scholar