Zariski second radical elements of lattice modules

Abstract

Let [Formula: see text] be a lattice module over a [Formula: see text]-lattice [Formula: see text]. In this paper, we introduce the concept of the Zariski second radical of elements of [Formula: see text] and investigate some properties of Zariski second radical of elements of [Formula: see text]. We also investigate when the Zariski second radical is equal to the second radical of elements of [Formula: see text]. We give a characterization of Noetherian space by using Zariski second radical of elements of [Formula: see text].