The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring

Abstract

Let R be a G-graded ring and M be a G-graded R-module. We define the graded primary spectrum of M , denoted by PSG(M ), to be the set of all graded primary submodules Q of M such that (GrM (Q) :R M ) = Gr((Q :R M )). In this paper, we define a topology on PSG(M ) having the Zariski topology on the graded prime spectrum SpecG(M ) as a subspace topology, and investigate several topological properties of this topological space.