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arXiv · 2208.01027

Specialization of Integral Closure of Ideals by General Elements

Lindsey Hill·Rachel Lynn
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Abstract

In this paper, we prove a result similar to results of Itoh and Hong-Ulrich, proving that integral closure of an ideal is compatible with specialization by a general element of that ideal for ideals of height at least two in a large class of rings. Moreover, we show integral closure of sufficiently large powers of the ideal is compatible with specialization by a general element of the original ideal. In a polynomial ring over an infinite field, we give a class of squarefree monomial ideals for which the integral closure is compatible with specialization by a general linear form.

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Lindsey Hill, Rachel Lynn. 2022-08-01. Specialization of Integral Closure of Ideals by General Elements. https://arxiv.org/abs/2208.01027

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