DING PROJECTIVE MODULES WITH RESPECT TO A SEMIDUALIZING MODULE
نویسندگان
چکیده
منابع مشابه
Gorenstein Projective Dimension with Respect to a Semidualizing Module
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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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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We prove versions of results of Foxby and Holm about modules of finite (Gorenstein) injective dimension and finite (Gorenstein) projective dimension with respect to a semidualizing module. We also verify special cases of a question of Takahashi and White. Mathematics Subject Classification (2000). 13C05, 13D05, 13H10.
متن کاملGorenstein Projective, Injective and Flat Modules Relative to Semidualizing Modules
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.
متن کاملSyzygy Modules with Semidualizing or G-projective Summands
Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R is Gorenstein if and only if some syzygy module of k has a G-projective summand.
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ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2014
ISSN: 1015-8634
DOI: 10.4134/bkms.2014.51.2.339