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

2025/04/13 by Yuya Otake, Otake, Yuya
Engineering · Mathematics · #13D02 #13D07 #16D90 #Commutative Algebra (math.AC) #Elasticity and Wave Propagation #FOS: Mathematics #Numerical methods in inverse problems #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2504.09505

openalex publication_date 2025/04/13 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Auslander developed a theory of the δ-invariant for finitely generated modules over commutative Gorenstein local rings, and Martsinkovsky extended this theory to the ξ-invariant for finitely generated modules over general commutative noetherian local rings. In this paper, we approach Martsinkovsky's ξ-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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