Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-06-01T17:36:45.552Z Has data issue: false hasContentIssue false
  • English
  • Français

On existence varieties of orthodox semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

J. Doyle
J. Doyle
Affiliation:
Department of Mathematics, Monash University, Clayton, Vic. 3168, Australia
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 existence variety of regular semigroups is a class of regular semigroups which is closed under the operations of forming all homomorphic images, all regular subsemigroups and all direct products. In this paper we generalize results on varieties of inverse semigroups to existence varieties of orthodox semigroups.

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups 20M17: Regular semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 1 , February 1995 , pp. 100 - 125
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Bales, J. L., ‘On product varieties of inverse semigroups’, J. Austral. Math. Soc.(Series A) 28 (1979), 107–119.Google Scholar
[2]Feigenbaum, R., Kernels of regular semigroup homomorphisms (Ph.D. Thesis, University of South Carolina, 1975).Google Scholar
[3]Feigenbaum, R., ‘Kernels of orthodox semigroup homomorphisms’, J. Austral. Math. Soc. (Series A) 22 (1976), 234–245.Google Scholar
[4]Feigenbaum, R., ‘Regular semigroup congruences’, Semigroup Forum 17 (1979), 373–377.Google Scholar
[5]Hall, T. E., ‘Congruences and Greens relations on regular semigroups’, Glasgow Math.J. 13 (1972), 167–175.CrossRefGoogle Scholar
[6]Hall, T. E., ‘On regular semigroups’, J. Algebra 24 (1973), 1–24.CrossRefGoogle Scholar
[7]Hall, T. E., ‘Identities for existence varieties of regular semigroups’, Bull. Austral. Math. Soc. 40 (1989), 59–77.CrossRefGoogle Scholar
[8]Howie, J. M., An introduction to semigroup theory (Academic Press, London, 1976).Google Scholar
[9]Howie, J. M. and Lallement, G., ‘Certain fundamental congruences on a regular semigroup’, Proc. Glasgow Math. Assoc. 7 (1976), 145–159.Google Scholar
[10]Kad'ourek, J. and Szendrai, M. B., ‘A new approach in the theory of orthodox semigroups’, Semi group Forum 40 (1990), 257–296.CrossRefGoogle Scholar
[11]Kleiman, E. I., ‘On the lattice of varieties of inverse semigroups’, Izv. Vyssh. Ucebn. Zaved. Mat. 7 (1976), 106–109.Google Scholar
[12]La Torre, D. R., ‘Group congruences on regular semigroups’, Semigroup Forum 24 (1982), 327–340.Google Scholar
[13]Meakin, J., ‘Congruences on orthodox semigrous’, J. Austral. Math. Soc. 12 (1971), 323–341.CrossRefGoogle Scholar
[14]Meakin, J., ‘Congruences on orthodox semigrous II’, J. Austral. Math. Soc. 13 (1972), 259–266.Google Scholar
[15]Pastijn, F. and Petrich, M., ‘Congruences on regular semigroups’, Trans. Amer. Math. Soc. 295 (1986), 607–633.CrossRefGoogle Scholar
[16]Pastijn, F. and Trotter, P. G., ‘Lattices of completely regular semigroup varieties’, Pacific J. Math. 119 (1985), 191–214.CrossRefGoogle Scholar
[17]Petrich, M., Introduction to semigroups (Merrill, Columbus, 1973).Google Scholar
[18]Petrich, M., Inverse semigroups (Wiley, New York, 1984).Google Scholar
[19]Reilly, N. R., ‘Modular sublattices of the lattice of varieties of inverse semigroups’, Pacific J. Math. 89 (1980), 405–417.Google Scholar
[20]Reilly, N. R., ‘Varieties of completely semisimple inverse semigroups’, J. Algebra 65 (1980), 427–444.CrossRefGoogle Scholar
[21]Reilly, N. R., ‘Minimal non-cryptic varieties of inverse semigroups’, Quart. J. Math. Oxford Ser. (2) 36 (1985), 467–487.Google Scholar
[22]Reilly, N. R. and Scheiblich, H. E., ‘Congruences on regular semigroups’, Pacific J. Math. 23 (1967), 349–360.CrossRefGoogle Scholar
[23]Saito, T., ‘Ordered regular proper semigroups’, J. Algebra 8 (1968), 450–477.CrossRefGoogle Scholar
[24]Scheiblich, H. E., ‘Certain congruence and quotient lattices related to completely 0-simple and primitive regular semigroups’, Glasgow Math. J. 10 (1969), 21–24.Google Scholar
[25]Szendrai, M. B., ‘On a pull-back diagram for orthodox semigroups’, Semigroup Forum 20 (1980), 1–10 Corrigendum: 25 (1982), 311–324.Google Scholar
[26]Szendrai, M. B., ‘Free*-orthodox semigroups’, Simon Stevin 59 (1985), 175–201.Google Scholar