Cohen-Macaulay injective, projective, and flat dimension
Henrik Holm, Peter Jorgensen
TL;DR
This paper introduces three new homological dimensions—Cohen-Macaulay injective, projective, and flat dimensions—that characterize Cohen-Macaulay rings with dualizing modules, expanding classical homological theory.
Contribution
It defines novel Cohen-Macaulay homological dimensions and establishes their role in characterizing Cohen-Macaulay rings with dualizing modules.
Findings
Finiteness of the new dimensions characterizes Cohen-Macaulay rings with dualizing modules.
The new dimensions form a theory analogous to classical homological dimensions.
Provides a framework for understanding Cohen-Macaulay properties via homological invariants.
Abstract
We define three new homological dimensions - Cohen-Macaulay injective, projective, and flat dimension - which inhabit a theory similar to that of classical injective, projective, and flat dimension. Finiteness of the new dimensions characterizes Cohen-Macaulay rings with dualizing modules.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons