A generalization of Maloo’s theorem on freeness
of derivation modules

We contribute to the theory of G-dimension relative to a semidualizing module [Formula: see text], in connection to the properties of a module being totally [Formula: see text]-reflexive, [Formula: see text]-[Formula: see text]-torsionless, and [Formula: see text]-[Formula: see text]-syzygy, where [Formula: see text] is an integer. We extend several known results, and for an integer [Formula: see text] we introduce the class of [Formula: see text]-[Formula: see text]-Gorenstein rings. We also consider [Formula: see text]-duals and initiate the study of [Formula: see text]-valued derivation modules over a local ring [Formula: see text] of low depth; if [Formula: see text] and [Formula: see text] is a three-dimensional Gorenstein domain, we find a bound for the number of generators and we propose a question when [Formula: see text] is general.

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A generalization of Maloo’s theorem on freeness of derivation modules

Cited by 2 publications

References 23 publications

Homological aspects of derivation modules and critical case of the Herzog–Vasconcelos conjecture

Homological aspects of derivation modules and critical case of the Herzog–Vasconcelos conjecture

On the theory and applications of G-dimension with respect to a semidualizing module

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