Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T17:15:02.394Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON THE HOWSON PROPERTY IN INVERSE SEMIGROUPS

Part of: Semigroups

Published online by Cambridge University Press:  16 August 2016

PETER R. JONES
PETER R. JONES*
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53201, USA email peter.jones@mu.edu
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 algebra has the Howson property if the intersection of any two finitely generated subalgebras is again finitely generated. A simple necessary and sufficient condition is given for the Howson property to hold on an inverse semigroup with finitely many idempotents. In addition, it is shown that any monogenic inverse semigroup has the Howson property.

Keywords

Howson propertyE-unitarymonogenic

MSC classification

Primary: 20M18: Inverse semigroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 457 - 463
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Brown, T. C., ‘An interesting combinatorial method in the theory of locally finite semigroups’, Pacific J. Math. 36 (1971), 285–289.CrossRefGoogle Scholar
Hall, T. E., ‘On regular semigroups’, J. Algebra 24 (1973), 1–24.CrossRefGoogle Scholar
Howson, A. G., ‘On the intersection of finitely generated free groups’, J. Lond. Math. Soc. (2) 29 (1954), 428–434.CrossRefGoogle Scholar
Jones, P. R., ‘Semimodular inverse semigroups’, J. Lond. Math. Soc. (2) 17 (1978), 446–456.CrossRefGoogle Scholar
Jones, P. R. and Trotter, P. G., ‘The Howson property for free inverse semigroups’, Simon Stevin 63 (1989), 277–284.Google Scholar
O’Carroll, L., ‘Embedding theorems for proper inverse semigroups’, J. Algebra 42 (1976), 26–40.CrossRefGoogle Scholar
Petrich, M., Inverse Semigroups (Wiley, New York, 1984).Google Scholar
Silva, P. V., Contributions to Combinatorial Semigroup Theory, PhD Thesis, University of Glasgow, 1991.Google Scholar
Silva, P. V. and Soares, F., ‘Howson’s property for semidirect products of semilattices by groups’, Comm. Algebra 44 (2016), 2482–2494.CrossRefGoogle Scholar