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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