Syzygy modules with semidualizing or G-projective summands
نویسندگان
چکیده
منابع مشابه
Syzygy 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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Article history: Received 26 March 2009 Available online 23 October 2010 Communicated by Efim Zelmanov MSC: 16E05 16E10
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We investigate the notion of the C-projective dimension of a module, where C is a semidualizing module. When C = R, this recovers the standard projective dimension. We show that three natural definitions of finite Cprojective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results th...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.01.012