Linearly equivalent topologies and locally quasi-unmixed rings

Authors : Adeleh AZARİ, Simin MOLLAMAHMOUDİ, Reza NAGHİPOUR

Pages : 1131-1136

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Publication Date : 2019-08-08

Article Type : Research Paper

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