Injective classes of modules

Wojciech Chachólski; Wolfgang Pitsch; Jérôme Scherer

doi:https://doi.org/10.1142/S0219498812501964

Injective classes of modules

Wojciech Chachólski, Wolfgang Pitsch, Jérôme Scherer

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring. © 2013 World Scientific Publishing Company.

Original language	English
Article number	1250188
Journal	Journal of Algebra and Its Applications
Volume	12
DOIs	https://doi.org/10.1142/S0219498812501964
Publication status	Published - 1 Jan 2013

Keywords

Injective classes
Noetherian ring
localizing subcategories
relative resolutions
smashing subcategories

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https://doi.org/10.1142/S0219498812501964

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abstract = "We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring. {\textcopyright} 2013 World Scientific Publishing Company.",

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AU - Chachólski, Wojciech

AU - Pitsch, Wolfgang

AU - Scherer, Jérôme

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AB - We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring. © 2013 World Scientific Publishing Company.

KW - Injective classes

KW - Noetherian ring

KW - localizing subcategories

KW - relative resolutions

KW - smashing subcategories

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DO - https://doi.org/10.1142/S0219498812501964

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JO - Journal of Algebra and Its Applications

JF - Journal of Algebra and Its Applications

SN - 0219-4988

M1 - 1250188

ER -

Injective classes of modules

Abstract

Keywords

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