2005•arXiv (Cornell University)Open access

Homological invariants associated to semi-dualizing bimodules

Tokuji Araya, Ryo Takahashi, Yuji Yoshino

Abstract

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.

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Key concepts: Noetherian, Local ring, Global dimension, Commutative property, Pure mathematics, Mathematics, Dimension (graph theory), Invariant (physics)