Using semidualizing complexes to detect Gorenstein rings
نویسندگان
چکیده
منابع مشابه
Gorenstein hereditary rings with respect to a semidualizing module
Let $C$ be a semidualizing module. We first investigate the properties of finitely generated $G_C$-projective modules. Then, relative to $C$, we introduce and study the rings over which every submodule of a projective (flat) module is $G_C$-projective (flat), which we call $C$-Gorenstein (semi)hereditary rings. It is proved that every $C$-Gorenstein hereditary ring is both cohe...
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In this paper we study some properties of GC -projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC -projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.
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We introduce and investigate the notion of GC -projective modules over (possibly non-noetherian) commutative rings, where C is a semidualizing module. This extends Holm and Jørgensen’s notion of C-Gorenstein projective modules to the non-noetherian setting and generalizes projective and Gorenstein projective modules within this setting. We then study the resulting modules of finite GC-projectiv...
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We study the following question: Given two semidualizing complexes B and C over a commutative noetherian ring R, does the vanishing of Ext R (B, C) for n ≫ 0 imply that B is C-reflexive? This question is a natural generalization of one studied by Avramov, Buchweitz, and Şega. We begin by providing conditions equivalent to B being C-reflexive, each of which is slightly stronger than the conditio...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2015
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-015-0769-y