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arXiv · 1607.07641

A Characterization of locally quasi-unmixed rings

Simin Mollamahmoudi·Adeleh Azari·Reza Naghipour
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Abstract

Let $\bar{I}$ denote the integral closure of an ideal in a Noetherian ring $R$. The main result of this paper asserts that $R$ is locally quasi-unmixed if and only if, the topologies defined by $\overline{I^n}$ and $I^{\langle n\rangle}$, $\ n\geq 1$, are equivalent. In addition, some results about the behavior of linearly equivalent topologies of ideals under various ring homomorphisms are included.

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Simin Mollamahmoudi, Adeleh Azari, Reza Naghipour. 2016-07-26. A Characterization of locally quasi-unmixed rings. https://arxiv.org/abs/1607.07641

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