Linearly equivalent topologies and locally quasi-unmixed rings

Year 2019, Volume: 48 Issue: 4, 1131 - 1136, 08.08.2019

Adeleh Azari Simin Mollamahmoudi Reza Naghipour

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.

Keywords

associated primes, linearly equivalent topologies, integral closure, locally quasi-unmixed ring, Rees ring

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