Linearly equivalent topologies andlocally quasi-unmixed rings

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 $I^{langle nrangle}$, $ ngeq 1$, are equivalent. In addition, some results about the behavior of linearly equivalent topologies of ideals under various ring homomorphisms are included.