Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-12T01:37:31.367Z Has data issue: false hasContentIssue false
  • English
  • Français

Basis properties for semigroups

Published online by Cambridge University Press:  18 May 2009

Peter R. Jones
Peter R. Jones
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI53233, U.S.A.
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.

A universal algebra A is said to have the basis property (BP) if any two minimal generating sets (bases) for a subalgebra of A have the same cardinality. This property was studied by the author for inverse semigroups in [5, 6]. For instance free inverse semigroups have BP. When treated as universal algebras, a classical theorem of linear algebra states that vector spaces have BP. In this paper we study BP for semigroups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 1 , January 1988 , pp. 101 - 109
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Burris, S. and Sankappanavar, H. P., A course in universal algebra, (Springer-Verlag, New York, 1981).CrossRefGoogle Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, (Math. Surveys of the Amer. Math. Soc. 7, Vol. 1, Providence R.I., 1961).Google Scholar
3.Doyen, J., Equipotence et unicité de systèmes générateurs minimaux dans certains monoides, Semigroup Forum 28 (1984), 341–346.CrossRefGoogle Scholar
4.Hall, T. E., On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195–208.CrossRefGoogle Scholar
5.Jones, P. R., A basis theorem for free inverse semigroups, J. Algebra 49 (1977), 172–190.CrossRefGoogle Scholar
6.Jones, P. R., Basis properties for inverse semigroups, J. Algebra 50 (1978), 135–152.CrossRefGoogle Scholar
7.Jones, P. R., Analogues of the bicyclic semigroup in simple semigroups without idempotents, Proc. Roy. Soc. Edinburgh, Sect. A 106 (1987) 11–24.CrossRefGoogle Scholar
8.Jones, P. R., Exchange properties and basis properties for closure operators (submitted).Google Scholar