Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-02T20:48:23.274Z Has data issue: false hasContentIssue false

Rees matrix semigroups and the regular semidirect product

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

K. Auinger
Affiliation:
Fakultät für MathematikUniversität WienNordbergstrasse 15A-1090 WienAustria e-mail: [email protected]
M. B. Szendrei
Affiliation:
Bolyai InstituteUniversity of SzegedAradi vértanúk tere 1H-6720 SzegedHungary e-mail: [email protected]
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 generalization of the Pastijn product is introduced so that, on the level of e-varieties and pseudoe-varieties, this product and the regular semidirect product by completely simple semigroups ‘almost always’ coincide. This is applied to give a model of the bifree objects in every e-variety formed as a regular semidirect product of a variety of inverse semigroups by a variety of completely simple semigroups that is not a group variety.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Auinger, K., ‘The bifree locally inverse semigroup on a set’, J. Algebra 166 (1994), 630650.CrossRefGoogle Scholar
[2]Auinger, K. and Polák, L., ‘A semidirect product for locally inverse semigroups’, Acta Sci. Math. 63 (1997), 405435.Google Scholar
[3]Auinger, K. and Szendrei, M. B., ‘Comparing the regular and the restricted regular semidirect pructs’, Algebra Universalis 51 (2004), 928.CrossRefGoogle Scholar
[4]Billhardt, B. and Szendrei, M. B., ‘Associativity of the regular semidirect product of existence varieties’, J. Austral. Math. Soc. Ser. A 69 (2000), 85115.CrossRefGoogle Scholar
[5]Billhardt, B., ‘Weakly E-unitary locally inverse semigroups’, J. Algebra 267 (2003), 559576.CrossRefGoogle Scholar
[6]Hall, T. E., ‘Identities for existence varieties of regular semigroups’, Bull. Austral. Math. Soc. 40 (1989), 5977.CrossRefGoogle Scholar
[7]Howie, J. M., Fundamentals of semigroup theory (Clarendon Press, Oxford, 1995).CrossRefGoogle Scholar
[8]Jones, P. R., ‘Rees matrix covers and semidirect products of regular semigroups’, J. Algebra 218 (1999), 287306.CrossRefGoogle Scholar
[9]Jones, P. R. and Trotter, P. G., ‘Semidirect products of regular semigroups’, Trans. Amer. Math. Soc. 349 (1997), 42654310.CrossRefGoogle Scholar
[10]Kadourek, J., ‘On some existence varieties of locally inverse semigroups’, Internat. J. Algebra Comput, 6 (1996), 761788.CrossRefGoogle Scholar
[11]Kadourek, J., ‘On some existence varieties of locally orthodox semigroups’, Internat. J. Algebra Comput, 7 (1997), 93131.CrossRefGoogle Scholar
[12]Kadourek, J. and Szendrei, M. B., ‘On existence varieties of E-solid semigroups’, Semigroup Forum 59 (1999), 470521.Google Scholar
[13]Khan, T. A. and Lawson, M. V., ‘Variants of regular semigroups’, Semigroup Forum 62 (2001), 358374.CrossRefGoogle Scholar
[14]Lawson, M. V., Inverse semigroups: the theory of partial symmetries (World Scientific, Singapore, 1998).CrossRefGoogle Scholar
[15]McAlister, D. B., ‘Rees matrix semigroups and regular Dubreil-Jacotin semigroups’, J. Austral. Math. Soc. Ser. A 31 (1981), 325336.CrossRefGoogle Scholar
[16]McAlister, D. B., ‘Rees matrix covers for locally inverse semigroups’, Trans. Amer. Math. Soc. 277 (1983), 727738.CrossRefGoogle Scholar
[17]Pastijn, F., ‘The structure of pseudo-inverse semigroups’, Trans. Amer. Math. Soc. 273 (1982), 631655.CrossRefGoogle Scholar
[18]Petrich, M., Inverse semigroups (Wiley & Sons, New York, 1984).Google Scholar
[19]Yeh, Y. T., ‘The existence of e-free objects in e-varieties of regular semigroups’, Internat. J. Algebra Comput 2 (1992), 471484.CrossRefGoogle Scholar