Injective classes of modules

Wojciech Chachólski; Wolfgang Pitsch; Jérôme Scherer

doi:10.1142/S0219498812501964

Injective classes of modules

Wojciech Chachólski^*, Wolfgang Pitsch, Jérôme Scherer

^*Corresponding author for this work

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.

Original language	American English
Article number	1250188
Journal	Journal of Algebra and its Applications
Volume	12
Issue number	4
DOIs	https://doi.org/10.1142/S0219498812501964
Publication status	Published - Jun 2013

Keywords

Injective classes
localizing subcategories
Noetherian ring
relative resolutions
smashing subcategories

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10.1142/S0219498812501964

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title = "Injective classes of modules",

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.",

keywords = "Injective classes, localizing subcategories, Noetherian ring, relative resolutions, smashing subcategories",

author = "Wojciech Chach{\'o}lski and Wolfgang Pitsch and J{\'e}r{\^o}me Scherer",

year = "2013",

month = jun,

doi = "10.1142/S0219498812501964",

language = "Ingl{\'e}s estadounidense",

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T1 - Injective classes of modules

AU - Chachólski, Wojciech

AU - Pitsch, Wolfgang

AU - Scherer, Jérôme

PY - 2013/6

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N2 - 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.

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.

KW - Injective classes

KW - localizing subcategories

KW - Noetherian ring

KW - relative resolutions

KW - smashing subcategories

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U2 - 10.1142/S0219498812501964

DO - 10.1142/S0219498812501964

M3 - Artículo

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SN - 0219-4988

VL - 12

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 4

M1 - 1250188

ER -

Injective classes of modules

Abstract

Keywords

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