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Hilbert multiplicity and irreducible multiplicity of idealizations (2311.04719v1)
Published 8 Nov 2023 in math.AC
Abstract: Let $(R,\mathfrak{m})$ be a Noetherian local ring and $M$ a finitely generated $R$-module. In this paper, we study the relation among the Hilbert function, Hilbert multiplicity, index of reducibility of an $\mathfrak{m}$-primary ideal, and the irreducible multiplicity under idealization $R\ltimes M$. Some applications to Cohen-Macaulayness and Cohen-Macaulay type of idealization are given.
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