Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T21:52:45.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Semidistributive inverse semigroups

Part of: Algebraic structures Semigroups

Published online by Cambridge University Press:  09 April 2009

Katherine G. Johnston-Thom  and
Peter R. Jones
Katherine G. Johnston-Thom
Affiliation:
Department of Mathematics University of Charleston, South Carolina Charleston South Carolina 29424USA e-mail: [email protected]
Peter R. Jones
Affiliation:
Department of Mathematics, Statistics and Computer Science Marquette UniversityMilwaukee Wisconsin 53233USA 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.

An inverse semigroup S is said to be meet (join) semidistributive if its lattice (S) of full inverse subsemigroups is meet (join) semidistributive. We show that every meet (join) semidistributive inverse semigroup is in fact distributive.

MSC classification

Secondary: 20M18: Inverse semigroups 08A30: Subalgebras, congruence relations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 1 , August 2001 , pp. 37 - 51
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Ershova, T. I., ‘Inverse semigroups with certain types of inverse subsemigroups’, Mat. Zap. Ural. Univ., Sverdlovsk 1 (1969), 62–76.Google Scholar
[2]Freese, R., Jezek, J. and Nation, J. B., Free lattices, Math. Surveys Monographs 42 (Amer. Math. Soc., Providence, 1995).Google Scholar
[3]Howie, J. M., Fundamentals of semigroups theory (Clarendon Press, Oxford, 1995).Google Scholar
[4]Johnston, K. G. and Jones, P. R., ‘Modular inverse semigroups’, J. Austral. Math. Soc. (Series A) 43 (1987), 47–63.Google Scholar
[5]Jones, P. R., ‘Semimodular inverse semigroups’, J. London Math. Soc. (2) 17 (1978), 446–456.Google Scholar
[6]Jones, P. R., ‘Distributive inverse semigroups’, J. London Math. Soc. (2) 17 (1978), 457–466.Google Scholar
[7]Jones, P. R., ‘Inverse semigroups and their lattices of inverse subsemigroups’, in: Lattices, semigroups and universal algebra (ed. Almeida, J. et al. ) (Plenum, New York, 1990).Google Scholar
[8]Napolitani, F., ‘Elementi U-quasidistributivi nel reticolo dei sottogruppi di un gruppo’, Ricerche Mat. 14 (1965), 93–101.Google Scholar
[9]Petrich, M., Inverse semigroups (Wiley, New York, 1984).Google Scholar
[10]Shevrin, L. N. and Ovsyannikov, A. J., Semigroups and their subsemigroups lattices (Kluwer, Dordrecht, 1996).Google Scholar
[11]Shiryaev, V. M., ‘Semigroups with λ-semidistributive subesmigroup lattice’, Semigroup Forum 31 (1985), 47–68.Google Scholar
[12]Suzuki, M., Structure of a group and the structure of its lattice of subgroups (Springer, Berlin, 1956).Google Scholar