On a relative dependency formula
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910654270537728 |
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| author | Sinha, Shashi Ranjan |
| author_facet | Sinha, Shashi Ranjan |
| contents | Celikbas, Liang and Sadeghi established a one-sided inequality for the relative version of Jorgensen's dependency formula and questioned whether it would be an equality. In this paper, we show that the inequality can be indeed strict, and prove a relative dependency formula. Along the way, we obtain some bounds on s(M,N), a notion related to the vanishing of relative homology of finitely generated modules M and N over a local ring R, under specific assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13239 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a relative dependency formula Sinha, Shashi Ranjan Commutative Algebra 13D02, 13D05, 13D07 Celikbas, Liang and Sadeghi established a one-sided inequality for the relative version of Jorgensen's dependency formula and questioned whether it would be an equality. In this paper, we show that the inequality can be indeed strict, and prove a relative dependency formula. Along the way, we obtain some bounds on s(M,N), a notion related to the vanishing of relative homology of finitely generated modules M and N over a local ring R, under specific assumptions. |
| title | On a relative dependency formula |
| topic | Commutative Algebra 13D02, 13D05, 13D07 |
| url | https://arxiv.org/abs/2410.13239 |