An approach to Martsinkovsky's invariant via Auslander's approximation theory
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916687966633984 |
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| author | Otake, Yuya |
| author_facet | Otake, Yuya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09505 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An approach to Martsinkovsky's invariant via Auslander's approximation theory Otake, Yuya Commutative Algebra Rings and Algebras Representation Theory 13D02, 16D90, 13D07 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. |
| title | An approach to Martsinkovsky's invariant via Auslander's approximation theory |
| topic | Commutative Algebra Rings and Algebras Representation Theory 13D02, 16D90, 13D07 |
| url | https://arxiv.org/abs/2504.09505 |