^{1}School of Mathematics, Statistics and Computer Science, College of Sciences, University of Tehran, Teheran, Iran

^{2}Department of Mathematics, Semnan University, Semnan, Iran

Abstract

Let $R$ be a commutative ring with identity and $M$ be an $R$-module. Let $FSpec(M)$ denotes the collection of all prime fuzzy submodules of $M$. In this regards some basic properties of Zariski topology on $FSpec(M)$ are investigated. In particular, we prove some equivalent conditions for irreducible subsets of this topological space and it is shown under certain conditions $FSpec(M)$ is a $T_0-$space or Hausdorff.

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