Some topological properties of spectrum of fuzzy submodules

Document Type : Research Paper


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

2 Department of Mathematics, Semnan University, Semnan, Iran


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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