Homological invariants associated to semi-dualizing bimodules

By Tokuji Araya, Ryo Takahashi, Yu Yoshino. 2005

77 citations recorded by the source corpus.

Cohen-Macaulay dimension for modules over a commutative 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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ae352d51cc4542b9f9920e288bd9772d5bf8c2c9

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Gorenstein projective dimension with respect to a semidualizing module (2006, background): “ic to Im(∂H 1 ι) which is contained in Im(∂H 1 ) ⊆ H0, contradicting assumption (3). The fact that γ0 is an isomorphism now follows as in [4, (8.5)]. Next we show that Madmits a resolution satisfying (1)–(3). With the ﬁrst part of this proof, this will establish part (a). First, note that by Corolla”
Comparison of relative cohomology theories with respect to semidualizing modules (2007, methodology): “R-module I). We let PC, FC and IC denote the categories of C-projective, C-ﬂat and C-injective R-modules, respectively. A complete PPC-resolution is a complex X of R-modules satisfying the following: (1) X is exact and HomR(−,PC)-exact, and (2) Xi is projective when i > 0 and Xi is C-projective w”
Foxby equivalence over associative rings (2006, background): “(a) When S is left noetherian and R is right noetherian, conditions (a1) and (a2) reduce to SC and CR being finitely generated, and therefore Definition 2.1 agrees with that of Araya-Takahashi-Yoshino [1, (2.1)].”