2021/03/21 by Kazuho Ozeki, Ozeki, Kazuho, Hoang Le Truong +3
Mathematics · #13A30 #13B22 #13H10 #13H15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #Secondary 13D45
paper · pdf · doi:10.48550/arxiv.2103.11334
openalex publication_date 2021/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we explore the relation between the index of reducibility and the Hilbert coefficients in local rings. Consequently, the main result of this study provides a characterization of a sequentially Cohen-Macaulay ring in terms of its Hilbert coefficients for non-parameter ideals. As corollaries to the main theorem, we obtain characterizations of a Gorenstein/Cohen-Macaulay ring in terms of its Chern coefficients for parameter ideals.