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arXiv · 2410.13239

On a relative dependency formula

Shashi Ranjan Sinha
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Abstract

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.

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Shashi Ranjan Sinha. 2024-10-17. On a relative dependency formula. https://arxiv.org/abs/2410.13239

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