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arXiv · 1505.04687

Sally Modules and Reduction Numbers of Ideals

Laura Ghezzi·Shiro Goto·Jooyoun Hong·Wolmer Vasconcelos
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Abstract

We study the relationship between the reduction number of a primary ideal of a local ring relative to one of its minimal reductions and the multiplicity of the corresponding Sally module. This paper is focused on three goals: (i) To develop a change of rings technique for the Sally module of an ideal to allow extension of results from Cohen-Macaulay rings to more general rings. (ii) To use the fiber of the Sally modules of almost complete intersection ideals to connect its structure to the Cohen-Macaulayness of the special fiber ring. (iii) To extend some of the results of (i) to two-dimensional Buchsbaum rings. Along the way we provide an explicit realization of the S_2-fication of arbitrary Buchsbaum rings.

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Laura Ghezzi, Shiro Goto, Jooyoun Hong, Wolmer Vasconcelos. 2015-05-18. Sally Modules and Reduction Numbers of Ideals. https://arxiv.org/abs/1505.04687

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