Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-29T22:43:29.034Z Has data issue: false hasContentIssue false
  • English
  • Français

Boolean Congruence Lattices of Orthodox Semigroups

Published online by Cambridge University Press:  20 November 2018

Karl Auinger
Karl Auinger*
Affiliation:
Institut für Mathematik Universität WienStrudlhofgasse 4 A-1090 Wien Austria
Rights & Permissions [Opens in a new window]

Extract

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.

The problem of characterizing the semigroups with Boolean congruence lattices has been solved for several classes of semigroups. Hamilton [9] and the author of this paper [1] studied the question for semilattices. Hamilton and Nordahl [10] considered commutative semigroups, Fountain and Lockley [7,8] solved the problem for Clifford semigroups and idempotent semigroups, in [1] the author generalized their results to completely regular semigroups. Finally, Zhitomirskiy [19] studied the question for inverse semigroups.

Keywords

20M1008A30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 225 - 241
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Auinger, K., Halbgruppen mit komplementaremKongruenzenverband. Doctoral Dissertation, University of Vienna, 1981.Google Scholar
2. Auinger, K., Semigroups with Boolean congruence lattices, Monatsh. Math. 104(1987), 1–15.Google Scholar
3. Auinger, K., Orthodox semigroups with complemented congruence lattices, Semigroup Forum 42(1991), 53- 57.Google Scholar
4. Bailes, G.L., Right inverse semigroups, J. Algebra 26(1973), 492–507.Google Scholar
5. Burns, S., Separating sets in modular lattices with applications to congruence lattices, Alg. Univ. 5(1975), 213–223.Google Scholar
6. Feigenbaum, R., Kernels of orthodox semigroup homomorphisms, J. Austral. Math. Soc. 22(1976), 234- 245.Google Scholar
7. Fountain, J. and Lockley, P., Semilattices of groups with distributive congruence lattice, Semigroup Forum 14(1977), 81–91.Google Scholar
8. Fountain, J. and Lockley, P., Bands with distributive congruence lattice, Proc. Royal Soc. Edinb. 84(1979), 235–247.Google Scholar
9. Hamilton, H., Semilattices whose structure lattice is distributive, Semigroup Forum 8(1974), 245–253.Google Scholar
10. Hamilton, H. and Nordhal, T., Semigroups whose lattice of congruences is Boolean, Pacific J. Math. 77(1978), 131–143.Google Scholar
11. Howie, J.M., An Introduction to Semigroup Theory. Academic Press, New York, 1976.Google Scholar
12. Meakin, J., Congruences on orthodox semigroups,]. Austral. Math. Soc. 12(1971), 323–341.Google Scholar
13. Mitsch, H., Semigroups and their lattices of congruences, Semigroup Forum 26(1983), 1–63.Google Scholar
14. Papert, D., Congruence relations in semilattices, J. London Math. Soc. 39(1964), 723–729.Google Scholar
15. Pastijn, F. and Petrich, M., Congruences on regular semigroups, Trans. Am. Math. Soc. 295(1986), 607–633.Google Scholar
16. Pastijn, F. and Petrich, M., The congruence lattice of a regular semigroup, J. Pure Appl. Alg. 53(1988), 93–123.Google Scholar
17. Petrich, M., Inverse Semigroups. Wiley, New York, 1984.Google Scholar
18. Petrich, M., Congruences on strong semilattices of simple regular semigroups, Semigroup Forum 37(1988), 167–199.Google Scholar
19. Zhitomirskiy, G. I., Generalized groups with a Boolean lattice of congruence relations, Upon Mnoz. i Resetki, Saratov Univ. 2(1974), 18-27. (Russian)Google Scholar