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Some characterizations of the hereditary pretorsion class of semigroup automata
Published online by Cambridge University Press: 18 May 2009
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.
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- Copyright © Glasgow Mathematical Journal Trust 1993
References
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