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NON-POINTED EXACTNESS, RADICALS, CLOSURE OPERATORS

Part of: Radicals and radical properties of rings General theory of categories and functors Ordered sets

Published online by Cambridge University Press:  07 June 2013

M. GRANDIS ,
G. JANELIDZE  and
L. MÁRKI
M. GRANDIS
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146-Genova, Italy email [email protected]
G. JANELIDZE
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa email [email protected]
L. MÁRKI*
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1364 Budapest, Pf. 127, Hungary
*
✉[email protected]
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Abstract

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In this paper it is shown how nonpointed exactness provides a framework which allows a simple categorical treatment of the basics of Kurosh–Amitsur radical theory in the nonpointed case. This is made possible by a new approach to semi-exactness, in the sense of the first author, using adjoint functors. This framework also reveals how categorical closure operators arise as radical theories.

Keywords

nonpointed exactnessnull morphismsadjoint functorsKurosh–Amitsur radicalscategorical closure operators

MSC classification

Secondary: 18A40: Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18A20: Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18A32: Factorization of morphisms, substructures, quotient structures, congruences, amalgams 18A99: None of the above, but in this section 16N80: General radicals and rings 06A15: Galois correspondences, closure operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 94 , Issue 3 , June 2013 , pp. 348 - 361
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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