Sally Modules of 𝔪-Primary Ideals in Local Rings

DOI10.1080/00927870802266490zbMATH Open1188.13002arXivmath/0309027OpenAlexW1534887496MaRDI QIDQ3656756

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Publication date: 14 January 2010

Published in: (Search for Journal in Brave)

Abstract: Given a local Noetherian ring $(R,mathfrakm)$ of dimension $d>0$ and infinite residue field, we study the invariants $($dimension and multiplicity$)$ of the Sally module $S_J(I)$ of any $mathfrakm$-primary ideal $I$ with respect to a minimal reduction $J$. As a by-product we obtain an estimate for the Hilbert coefficients of $mathfrakm$ that generalizes a bound established by J. Elias and G. Valla in a local Cohen-Macaulay setting. We also find sharp estimates for the multiplicity of the special fiber ring $mathcalF(I)$, which recover previous bounds established by C. Polini, W.V. Vasconcelos and the author in the local Cohen-Macaulay case. Great attention is also paid to Sally modules in local Buchsbaum rings.

Full work available at URL: https://arxiv.org/abs/math/0309027

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