October 13, 2025Open Access

Integral closure of 1-dimensional rings

Key Points

The study reveals important links between the order of the conductor ideal and multiplicity in local integral domains.
We examine reflexivity in colength-two ideals, providing insight into their structure and properties.
The research connects the freeness problem of absolute integral closure of DVR with reflexivity issues in specific rings.
Understanding these properties could advance theories in algebraic geometry and commutative algebra.

Abstract

We study certain properties of modules over 1-dimensional local integral domains. First, we examine the order of the conductor ideal and its expected relationship with multiplicity. Next, we investigate the reflexivity of certain colength-two ideals. Finally, we consider the freeness problem of the absolute integral closure of a DVR, and connect this to the reflexivity problem of R^1{pⁿ}.

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Cite This Study

Mohsen Asgharzadeh (Mon,) studied this question.

synapsesocial.com/papers/68ece2abd1bb2827d1297316 https://doi.org/https://doi.org/10.48550/arxiv.2503.01640

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