Abstract
The torsion theory for semi-automata in a general sense or acts, as developed in [4], is further investigated. After recalling some of the basic concepts and results of that theory it is proved by means of a lemma on Galois connections in general that the torsion classes, the torsionfree classes, and the torsion theories of semi-automata of an appropriate category form a complete lattice. These lattices are isomorphic to each other or to the dual; they are considered in more detail: it is shown that the abstract classes of irreducible acts form a complete atomistic Boolean sublattice; further a proof is given that the simple abelian groups are characterized as those groups whose lattice of torsion theories for the corresponding group acts is a pentagon.
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Dedicated with gratitude to Prof. Dr. rer. nat. habil. Dr. phil. H.J. Weinert on the occasion of his 60th birthday
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© 1987 D. Reidel Publishing Company
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Lex, W. (1987). Lattices of Torsion Theories for Semi-Automata. In: Goberstein, S.M., Higgins, P.M. (eds) Semigroups and Their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3839-7_11
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DOI: https://doi.org/10.1007/978-94-009-3839-7_11
Publisher Name: Springer, Dordrecht
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