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arXiv · 1711.05399

Descending chains of semistar operations

Hyun Seung Choi·Timothy McEldowney·Andrew Walker
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Abstract

A class of integer-valued functions defined on the set of ideals of an integral domain $R$ is investigated. We show that this class of functions, which we call ideal valuations, are in one-to-one correspondence with countable descending chains of finite type, stable semistar operations with largest element equal to the $e$-operation. We use this class of functions to recover familiar semistar operations such as the $w$-operation and to give a solution to a conjecture by Chapman and Glaz when the ring is a valuation domain.

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Hyun Seung Choi, Timothy McEldowney, Andrew Walker. 2017-11-15. Descending chains of semistar operations. https://arxiv.org/abs/1711.05399

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