This research investigates the relationship between conductor ideals and multiplicity in 1-dimensional rings, exploring reflexivity implications.
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 R1/pⁿ.
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Mohsen Asgharzadeh (2025) studied this question.
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