Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-11T10:00:23.850Z Has data issue: false hasContentIssue false
  • English
  • Français

Matrix representations of semigroups

Published online by Cambridge University Press:  18 May 2009

D. B. McAlister
D. B. McAlister
Affiliation:
Department of Pure MathematicsQueen's UniversityBelfast
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.

In a series of papers [6], [7], [8], [10], Munn has considered the problem of constructing all irreducible representations of a semigroup by matrices over a field. In [10], he showed how to construct all the irreducible representations of an arbitrary inverse semigroup from those of associated Brandt semigroups. In this paper, we generalize the method of [10] to give a construction for the irreducible representations of an arbitrary semigroup from those of certain associated semigroups

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 8 , Issue 1 , January 1967 , pp. 1 - 13
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

1.Clifford, A. H., Matrix representations of completely 0-simple semigroups, American J. Math. 64 (1942), 327–342.Google Scholar
2.Clifford, A. H. and Preston, G. B., Algebraic theory of semigroups, Vol. 1, American Math. Soc. Surveys, 7 (1961).CrossRefGoogle Scholar
3.Green, J. A., On the structure of semigroups, Ann. of Math. 54 (1951), 163–172.Google Scholar
4.Lallement, G., Sur les homomorphismes d'un demigroupe sur un demigroupe completement 0-simple, Seminaire Dubreil-Pisot, 1963–64, no. 14.Google Scholar
5.Lallement, G. and Petrich, M., Some results concerning completely O-simple semigroups, Bull. Amer. Math. Soc. 70 (1964), 777–778.CrossRefGoogle Scholar
6.Munn, W. D., Matrix representations of semigroups, Proc. Cambridge Phil. Soc. 53 (1957), 145–152.CrossRefGoogle Scholar
7.Munn, W. D., Irreducible matrix representations of semigroups, Quart. J. Math. (Oxford Ser.) (2) 11 (1960), 295–309.Google Scholar
8.Munn, W. D., A class of irreducible matrix representations ofan arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48.CrossRefGoogle Scholar
9.Munn, W. D., Brandt congruences on inverse semigroups, Proc. London Math. Soc. (3) 14 (1964), 154–164.Google Scholar
10.Munn, W. D., Matrix representations of inverse semigroups, Proc. London Math. Soc. (3) 14 (1964), 165–181.CrossRefGoogle Scholar
11.Preston, G. B., Congruences on semigroups (Ed. Howie, J. M.), N.S.F. Algebra Institute. Pennsylvania State University, Summer 1963.Google Scholar