Specialization of integral closure of ideals by general elements

Hill, Lindsey; Lynn, Rachel

doi:10.1090/proc/16697

Specialization of integral closure of ideals by general elements
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by Lindsey Hill and Rachel Lynn;

Proc. Amer. Math. Soc. 152 (2024), 1893-1906

DOI: https://doi.org/10.1090/proc/16697

Published electronically: March 7, 2024

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Abstract:

In this paper, we prove a result similar to results of Itoh [J. Algebra 150 (1992), pp. 101–117] and Hong-Ulrich [J. Lond. Math. Soc. (2) 90 (2014), pp. 861–878], 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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