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On a Conjecture Concerning Semigroup Homomorphisms

Published online by Cambridge University Press:  20 November 2018

R. J. Plemmons
R. J. Plemmons*
Affiliation:
The University of Tennessee, Knoxville, Tennessee
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In this paper we settle (with a counterexample) the question raised by Clifford and Preston in [2, p. 275], concerning maximal group homomorphic images of semigroups. We also consider the question in a more general context and characterize all such examples. The notation and definitions follow [1; 2].

By a type of semigroups we mean a class of semigroups, closed under isomorphisms and containing the one-element semigroup. If S is any semigroup and is a type, then a semigroup S* is defined, in [1, p. 18], to be a maximal homomorphic image of S having type if

(i) ,

(ii) S* is a homomorphic image of S, and

(iii) whenever and T is a homomorphic image of S, then there exists a homomorphism from S* onto T.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 641 - 644
Copyright
Copyright © Canadian Mathematical Society 1970

References

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