Irreducible multiplicity of idealizations

2023/11/08 by Tran Nguyen An, An, Tran Nguyen
Mathematics · #13A15 #13H10 #13H15 #Algebra over a field #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Hilbert series and Hilbert polynomial #Hilbert space #Hilbert–Poincaré series #Idealization #Local ring #Mathematical analysis #Mathematics #Multiplicity (mathematics) #Noetherian #Physics #Pure mathematics #Quantum mechanics #Ring (chemistry)

paper · pdf · doi:10.48550/arxiv.2311.04719

openalex publication_date 2023/11/08 · openalex created_date 2023/11/10 · openalex updated_date 2026/07/28

Abstract

Let (R,\mathfrakm) be a Noetherian local ring and M a finitely generated R-module. We study the relations of the index of reducibility and the irreducible multiplicity of an \mathfrakm-primary ideal of R and these of \mathfrakm × M-primary ideal of the idealization. This generalizes one of the main results of S.Goto et al. (see \cite[Theorem 2.2]GKL).

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