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The Sally module of an ideal is an important tool to interplay betweenHilbert coefficients and the properties of the associated graded ring. In thispaper we give new insights on the structure of the Sally module. We apply theseresults characterizing the almost minimal value of the first Hilbertcoefficient in the case of the normal filtration in an analytically unramifiedCohen-Macaulay local ring.

A filtration of the Sally module and the First normal Hilbert Coefficient