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Primitive homomorphic images of semigroups

Published online by Cambridge University Press:  09 April 2009

T. E. Hall
T. E. Hall
Affiliation:
Department of MathematicsMonash University, Clayton
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Consideration of the primitive homomorphic images of semigroups arises naturally from their matrix representation theory. (See, for example, papers [1] and [2].) This is basically because a semigroup of matrices, in which all the matrices have the same rank, is necessarily primitive. (The set of idempotents in the semigroup may be empty, however).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 2 , May 1968 , pp. 350 - 354
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Munn, W. D., Matrix representations of inverse semigroups, Proc. London Math. Soc. 14 (1964). 165–181.CrossRefGoogle Scholar
[2]Preston, G. B., Matrix representations of inverse semigroups, J. Aust. Math. Soc. (to appear).Google Scholar
[3]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys, number 7, Amer. Math. Soc. 1961).Google Scholar
[4]Lallement, G.. Congruences et équivalences de Green sur un demi-groupe régulier, C. R. Acad. Sc. Paris, Série A, 262 (1966), 613–616.Google Scholar