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A note on shortly connected inverse semigroups

Published online by Cambridge University Press:  17 April 2009

S.M. Goberstein
S.M. Goberstein
Affiliation:
Department of Mathematics and Statistics, California State University, Chico Chico, California 95929-0525, United States of America
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Abstract

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Shortly connected and shortly linked inverse semigroups arise in the study of inverse semigroups determined by the lattices of inverse subsemigroups and by the partial automorphism semigroups. It has been shown that every shortly linked inverse semigroup is shortly connected, but the question of whether the converse is true has not been addressed. Here we construct two examples of combinatorial shortly connected inverse semigroups which are not shortly linked. One of them is completely semisimple while the other is not.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 463 - 466
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Goberstein, S.M., ‘Inverse semigroups with isomorphic partial automorphism semigroups’, J. Austral. Math. Soc. (Ser. A) 47 (1989), 399–417.CrossRefGoogle Scholar
[2]Howie, J.M., An introduction to semigroup theory (Academic Press, London, 1976).Google Scholar
[3]Petrich, M., Inverse semigroups (Wiley, New York, 1984).Google Scholar