Weakly Hereditary Initial Closure Operators

Temple H. Fay ()
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Temple H. Fay: University of Southern Mississippi, Department of Mathematics

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 415-431 from Springer

Abstract: Abstract We extend some recent of M. M. Clementino (Topology and its Applications 49 (1993)) and of the author (Cahiers de Topologie et Géométrie Différentielle Catégoriques XXXVII(4) (1996)) concerning when a regular closure operator is weakly hereditary. In this work, we study initial closure operators which include both regular and normal closure operators. Working in a quasi-additive regular category in which pullbacks of cokernels are cokernels, we characterize when they initial closure operators are weakly hereditary. For the category of all groups, we show that a non-trivial normal closure operator is never weakly hereditary.

Keywords: 18A40; 18E40; closure operator; regular closure operator; normal closure operator; weakly hereditary closure operator; generalized torsion theory. (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_25

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DOI: 10.1007/978-94-017-2529-3_25

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