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Free Objects in Certain Varieties of Inverse Semigroups

Published online by Cambridge University Press:  20 November 2018

S. W. Margolis ,
J. C. Meakin  and
J. B. Stephen
S. W. Margolis
Affiliation:
Department of Computer Science, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, U.S.A.
J. C. Meakin
Affiliation:
Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, U.S.A.
J. B. Stephen
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60615, U.S.A.
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Abstract

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In this paper it is shown how the graphical methods developed by Stephen for analyzing inverse semigroup presentations may be used to study varieties of inverse semigroups. In particular, these methods may be used to solve the word problem for the free objects in the variety of inverse semigroups generated by the five-element combinatorial Brandt semigroup and in the variety of inverse semigroups determined by laws of the form xn = xn + 1. Covering space methods are used to study the free objects in a variety of the form ∨ where is a variety of inverse semigroups and is the variety of groups.

Keywords

20M0520M1803D40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 6 , 01 December 1990 , pp. 1084 - 1097
Copyright
Copyright © Canadian Mathematical Society 1990

Footnotes

Research supported by N.S.F. grant DMS 8702019.

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