Hilbert functions of socle ideals
Hoang Le Truong, Hoang Ngoc Yen
TL;DR
This paper investigates the relationship between Hilbert functions and ideal decompositions in local rings, providing characterizations of key properties like regularity, Gorensteinness, and Cohen-Macaulayness.
Contribution
It introduces new connections between Hilbert functions and irreducible decompositions, offering criteria for important ring properties.
Findings
Characterizes regularity, Gorensteinness, Cohen-Macaulayness, and sequentially Cohen-Macaulayness using Hilbert functions
Establishes a link between Hilbert functions and irreducible decompositions of ideals
Provides applications to classify local ring properties
Abstract
In this paper, we explore a relationship between Hilbert functions and the irreducible decompositions of ideals in local rings. Applications are given to characterize the regularity, Gorensteinness, Cohen-Macaulayness and sequentially Cohen-Macaulayness of local rings.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Polynomial and algebraic computation