Multiplicities in flat local extensions

Abstract: We introduce the notion of strongly Lech-independent ideals as a generalization of Lech-independent ideals defined by Lech and Hanes, and use this notion to derive inequalities on multiplicities of ideals. In particular we prove that if (R,m) and (S,n) are Noetherian local rings of the same dimension, S is a flat local extension of R,and up to completion S is standard graded over a field and I=mS is homogeneous, then the multiplicity of R is no greater than that of S.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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