Geodesic
Some characterizations of the hereditary pretorsion class of semigroup automata
Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 327-337

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Lam, Clement S. Some characterizations of the hereditary pretorsion class of semigroup automata. Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 327-337. doi: 10.1017/S0017089500009903
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