Hostname: page-component-5db58dd55d-mhzq2 Total loading time: 0 Render date: 2026-05-27T22:15:08.531Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse semigroups whose full inverse subsemigroups form a chain

Published online by Cambridge University Press:  18 May 2009

P. R. Jones
P. R. Jones
Affiliation:
Department of Mathematics, Monash University Clayton, Victoria Australia 3168
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 structure of semigroups whose subsemigroups form a chain under inclusion was determined by Tamura [9]. If we consider the analogous problem for inverse semigroups it is immediate that (since idempotents are singleton inverse subsemigroups) any inverse semigroup whose inverse subsemigroups form a chain is a group. We will therefore, continuing the approach of [5, 6], consider inverse semigroups whose full inverse subsemigroups form a chain: we call these inverse ▽-semigroups.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 2 , July 1981 , pp. 159 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Surveys of the Amer. Math. Soc. 7 (Providence, R.I., 1961 (Vol. I) and 1967 (vol. II)).Google Scholar
2.Eberhart, C., Elementary orthodox semigroups, Proc. Symposium on Inverse Semigroups and their Generalizations, Northern Illinois University, 1973, 23–33.Google Scholar
3.Fuchs, L., Abelian groups (Pergamon Press, 1960).Google Scholar
4.Howie, J. M., An introduction to semigroup theory, (Academic Press, 1976).Google Scholar
5.Jones, P. R., Semimodular inverse semigroups, J. London Math. Soc. 17 (1978), 446–456.CrossRefGoogle Scholar
6.Jones, P. R., Distributive inverse semigroups, J. London Math. Soc. 17 (1978), 457–466.CrossRefGoogle Scholar
7.McAlister, D. B., Groups, semilattices and inverse semigroups II, Trans. Amer. Math. Soc. 196 (1974), 351–370.CrossRefGoogle Scholar
8.Meakin, J., One-sided congruences on inverse semigroups, Trans. Amer. Math. Soc. 206 (1975), 67–82.CrossRefGoogle Scholar
9.Tamura, T., On a monoid whose submonoids form a chain, J. Gakugei Tokushima Univ. 5 (1954), 8–16.Google Scholar
10.Tamura, T., Commutative semigroups whose lattice of congruences is a chain. Bull. Soc. Math. France 97 (1969), 369–380.CrossRefGoogle Scholar