An approach to Martsinkovsky's invariant via Auslander's approximation theory

Yuya Otake

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arXiv · 2504.09505

An approach to Martsinkovsky's invariant via Auslander's approximation theory

Yuya Otake

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Abstract

Auslander developed a theory of the $\delta$-invariant for finitely generated modules over commutative Gorenstein local rings, and Martsinkovsky extended this theory to the $\xi$-invariant for finitely generated modules over general commutative noetherian local rings. In this paper, we approach Martsinkovsky$'$s $\xi$-invariant by considering a non-decreasing sequence of integers that converges to it. We investigate Auslander$'$s approximation theory and provide methods for computing this non-decreasing sequence using the approximation.

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Yuya Otake. 2025-04-13. An approach to Martsinkovsky's invariant via Auslander's approximation theory. https://arxiv.org/abs/2504.09505

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