Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T17:36:55.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Residual finiteness of free products of combinatorial strict inverse semigroups

Published online by Cambridge University Press:  14 November 2011

Karl Auinger
Karl Auinger
Affiliation:
Institut für Mathematik, Strudlhofgasse 4, A-1090 Wien, Austria
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that the free product of two residually finite combinatorial strict inverse semigroups in general is not residually finite. In contrast, the free product of a residually finite combinatorial strict inverse semigroup and a semilattice is residually finite.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 1 , 1994 , pp. 137 - 147
Copyright
Copyright © Royal Society of Edinburgh 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Auinger, K.. The congruence lattice of a strict regular semigroup. J. Pure Appl. Algebra 81 (1992), 219–245.CrossRefGoogle Scholar
2Auinger, K.. Free strict inverse semigroups. J. Algebra 157 (1993), 26–42.Google Scholar
3Auinger, K.. Free products of combinatorial strict inverse semigroups. Pacific J. Math. (to appear).Google Scholar
4Jones, P. R., Margolis, S. W., Meakin, J. C. and Stephen, J. B.. Free products of inverse semigroups II. Glasgow Math. J. 33 (1991), 373–387.CrossRefGoogle Scholar
5Nambooripad, K. S. S.. Pseudo-semilattices and biordered sets III: Regular locally testable semigroups. Simon Stevin 56 (1982), 239–256.Google Scholar
6Petrich, M.. Inverse Semigroups (New York: Wiley, 1984).Google Scholar