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INTEGRAL CLOSURE OF STRONGLY GOLOD IDEALS

Part of: Ring extensions and related topics Commutative algebra: Homological methods General commutative ring theory

Published online by Cambridge University Press:  18 July 2019

CĂTĂLIN CIUPERCĂ Open the ORCID record for CĂTĂLIN CIUPERCĂ [Opens in a new window]
CĂTĂLIN CIUPERCĂ*
Affiliation:
Department of Mathematics 2750, North Dakota State University, PO BOX 6050, Fargo, ND 58108-6050, USA email catalin.ciuperca@ndsu.edu
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Abstract

We prove that the integral closure of a strongly Golod ideal in a polynomial ring over a field of characteristic zero is strongly Golod, positively answering a question of Huneke. More generally, the rational power $I_{\unicode[STIX]{x1D6FC}}$ of an arbitrary homogeneous ideal is strongly Golod for $\unicode[STIX]{x1D6FC}\geqslant 2$ and, if $I$ is strongly Golod, then $I_{\unicode[STIX]{x1D6FC}}$ is strongly Golod for $\unicode[STIX]{x1D6FC}\geqslant 1$. We also show that all the coefficient ideals of a strongly Golod ideal are strongly Golod.

MSC classification

Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13B22: Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)
Secondary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series

Information

Type
Article
Information
Nagoya Mathematical Journal , Volume 241 , March 2021 , pp. 204 - 216
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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