Katharine Shultis

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20142022

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math.AC2019

Reducibility of parameter ideals in low powers of the maximal ideal

Katharine Shultis, Peder Thompson

A commutative noetherian local ring $(R, m)$ is Gorenstein if and only if every parameter ideal of $R$ is irreducible. Although irreducible parameter ideals may exist in…

math.AC2014

Systems of Parameters and the Cohen-Macaulay Property

Katharine Shultis

Let $R$ be a commutative, Noetherian, local ring and $M$ an $R$ -module. Consider the module of homomorphisms $Hom_{R} (R / a, M / b M)$ where $\mathfra…