### On the Spectrum of weakly prime submodule

#### Abstract

A proper submodule P of an R-module M is called a weakly prime submodule , if for each

submodule K of M and elements a,b of R , abK P implies that aK P or bK

P. Let WSpec(M) be the set of all weakly prime submodules of M . In this paper , a

topology on WSpec(M) is introduced. We investigate some basic properties of the open

and closed sets in that topology and establish their relationships with weakly prime radical

and Flat Module. We also investigate some topological properties in WSpec(M) such as

connectedness,separation axioms etc. Finally we try to characterize the spectrum of weakly

prime submodule with the help of quasi multiplication module. we prove that if M is a

nitely generated quasi multiplication R-module then WSpec(M) is compact.

submodule K of M and elements a,b of R , abK P implies that aK P or bK

P. Let WSpec(M) be the set of all weakly prime submodules of M . In this paper , a

topology on WSpec(M) is introduced. We investigate some basic properties of the open

and closed sets in that topology and establish their relationships with weakly prime radical

and Flat Module. We also investigate some topological properties in WSpec(M) such as

connectedness,separation axioms etc. Finally we try to characterize the spectrum of weakly

prime submodule with the help of quasi multiplication module. we prove that if M is a

nitely generated quasi multiplication R-module then WSpec(M) is compact.

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