Exactness of cochain complexes via additive functors

Federico Campanini; Alberto Facchini

doi:10.4134/CKMS.c200069

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Exactness of cochain complexes via additive functors

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참고문헌

키워드

Relative exactness of sequences spectral category

주제분류수학

초록

We investigate the relation between the notion of $e$-exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor $P\colon\Mod R\to \Spec(\Mod R)$, where $\Spec(\Mod R)$ denotes the spectral category of $\Mod R$, and the localization functor with respect to the singular torsion theory.

Abstract

We investigate the relation between the notion of $e$-exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor $P\colon\Mod R\to \Spec(\Mod R)$, where $\Spec(\Mod R)$ denotes the spectral category of $\Mod R$, and the localization functor with respect to the singular torsion theory.

참고문헌 (9)

Ismael Akray, "Essential exact sequences", 대한수학회논문집, 35(2), pp.469~480 (2020), 대한수학회[DOI]
M. J. Arroyo Paniagua, "Rings and Factorizations", pp.135~152 (2020), Springer
A. Facchini, "Module theory" (1998), Birkhäuser Verlag
T. Fritz, "Categories of fractions revisited", Morfismos, 15(2), pp.19~38 (2011)
P. Gabriel, "Spektralkategorien und reguläre Ringe im von-Neumannschen Sinn", Math. Z, 92, pp.389~395 (1966)[DOI]
P. Gabriel, "Calculus of fractions and homotopy theory" (1967), Springer-Verlag New York, Inc
K. R. Goodearl, "Ring Theory" (1976), Marcel Dekker, Inc.
T. Y. Lam, "Lectures on Modules and Rings" (1999), Springer-Verlag
B. Stenström, "Rings of Quotients" (1975), Springer-Verlag

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