Grothendieck groups arising from contravariantly finite subcategories
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Beligiannis, A.
Marmaridis, N.
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Taylor & Francis
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peer reviewed
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Communications in Algebra
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The subject of the paper is the study of the relative homological properties of a given additive category C in relation to a given contravariantly finite subcategory chi in C under the assumption that any chi-epic has a kernel in C. We introduce the notion of the Grothendieck group relative to the pair (C, chi) and also that of the Cartan map c chi relative to (C, chi) and we show that the cokernel of c chi is isomorphic to the corresponding Grothendieck group of the stable category C/J chi. We also show that if the right chi-dimension of C is finite, then c chi is an isomorphism. In case C is a finite dimensional k-additive Krull-Schmidt category, we introduce the notion of the chi-dimension vector of an object of C. We give criteria for when an indecomposable object is determined, up to isomorphism, by its chi-dimension vector.
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algebras, modules
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<Go to ISI>://A1996VY71700009
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en
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Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών