Lattices of Torsion Theories for Semi-Automata

Wilfried Lex
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Wilfried Lex: Technische Universität Clausthal, Institut für Informatik

A chapter in Semigroups and Their Applications, 1987, pp 83-90 from Springer

Abstract: 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.

Date: 1987
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DOI: 10.1007/978-94-009-3839-7_11

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