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Some characterizations of the hereditary pretorsion class of semigroup automata

Published online by Cambridge University Press:  18 May 2009

Clement S. Lam
Clement S. Lam
Affiliation:
Department of MathematicsIthaca CollegeIthaca, NY 14850U.S.A.
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Abstract

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Let S be a semigroup. A class of S-automata is called a hereditary pretorsion class (HPC) if it is closed under quotients, subautomata, coproducts (disjoint unions) and finite products. In this paper we present two characterizations of HPC. Specifically, we show that there is a bijective correspondence between the HPCs of S-automata, the right linear topologies on S′ and the idempotent preradicals r on the category of S-automata such that the set of automata {M|r(M) = M} is closed under subautomata and finite products.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 327 - 337
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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