Generation in Module Categories and Derived Categories of Commutative Rings

Ryo Takahashi ()
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Ryo Takahashi: Nagoya University, Graduate School of Mathematics

A chapter in Commutative Algebra, 2021, pp 723-750 from Springer

Abstract: Abstract Let R be a ring, and let M, N be R-modules. It is a natural question to ask whether or how one can build M out of N by iteration of fundamental operations such as direct sums, direct summands and extensions. It is possible to think of this question not only in module categories but also in derived categories. In this article we consider the question in the case where R is a commutative noetherian ring.

Keywords: Module category; Derived category; Singularity category; Contravariantly finite subcategory; Resolving subcategory; Thick subcategory; Dimension; Radius; Cohen–Macaulay ring; Gorenstein ring; Complete intersection; Hypersurface; 13C60; 13D09; 13H10 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_24

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DOI: 10.1007/978-3-030-89694-2_24

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