Cohen-Macaulay dimension for modules over a commutative noetherian local ring
has been defined by A. A. Gerko. That is a homological invariant sharing many
properties with projective dimension and Gorenstein dimension. The main purpose
of this paper is to extend the notion of Cohen-Macaulay dimension for modules
over commutative noetherian local rings to that for bounded complexes over
non-commutative noetherian rings.Comment: 19 pages, to appear in J. Math. Kyoto Uni

Araya, Tokuji

Takahashi, Ryo

Yoshino, Yuji

English

arXiv

Tokuji Araya

Ryo Takahashi

Yuji Yoshino

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Homological invariants associated to semi-dualizing bimodules

Zhen Zhang

Xiaosheng Zhu

Xiaoguang Yan

Czechoslovak Mathematical Journal

Totally reflexive modules with respect to a semidualizing bimodule

summary:Let $S$ and $R$ be two associative rings, let $ _{S}C_{R}$ be a semidualizing $(S,R)$-bimodule. We introduce and investigate properties of the totally reflexive module with respect to $_{S}C_{R}$ and we give a characterization of the class of the totally $C_{R}$-reflexive modules over any ring $R$. Moreover, we show that the totally $C_{R}$-reflexive module with finite projective dimension is exactly the finitely generated projective right $R$-module. We then study the relations between the class of totally reflexive modules and the Bass class with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting

Homological invariants associated to semi-dualizing bimodules

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