Finitely Generated Modules and Connectivity

Abstract Let 𝑅 be a commutative Noetherian ring and let 𝑀 be a finitely generated 𝑅-module. Let 𝑋 = Spec𝑅(𝑀) be the topological space with Zariski topology. Our main goal in this paper is to describe the connectedness dimension of 𝑅 in terms of Krull dimension of some quotient of 𝑀 and prove that 𝑐(Spec𝑅(𝑀)) = 𝑐(Supp(𝑀)).