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April, 2021 Auslander's formula for contravariantly finite subcategories
Javad ASADOLLAHI, Rasool HAFEZI, Mohammad Hossein KESHAVARZ
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J. Math. Soc. Japan 73(2): 329-349 (April, 2021). DOI: 10.2969/jmsj/83308330

Abstract

Let $A$ be a right coherent ring and $\mathcal{X}$ be a contravariantly finite subcategory of ${\rm{mod}}\mbox{-}A$ containing projectives. In this paper, we construct a recollement of abelian categories $({\rm{mod}}_{0}\mbox{-}\mathcal{X}, {\rm{mod}}\mbox{-}\mathcal{X}, {\rm{mod}}\mbox{-}A)$, where ${\rm{mod}}_{0}\mbox{-}\mathcal{X}$ is a full subcategory of ${\rm{mod}}\mbox{-}\mathcal{X}$ consisting of all functors vanishing on projective modules. As a result, a relative version of Auslander's formula with respect to a contravariantly finite subcategory will be given. Some examples and applications will be provided.

Funding Statement

This research was in part supported by a grant from IPM.

Citation

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Javad ASADOLLAHI. Rasool HAFEZI. Mohammad Hossein KESHAVARZ. "Auslander's formula for contravariantly finite subcategories." J. Math. Soc. Japan 73 (2) 329 - 349, April, 2021. https://doi.org/10.2969/jmsj/83308330

Information

Received: 11 September 2019; Published: April, 2021
First available in Project Euclid: 23 January 2021

Digital Object Identifier: 10.2969/jmsj/83308330

Subjects:
Primary: 18A25
Secondary: 16G10, 16S50

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 2 • April, 2021
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