On the Spectrum of weakly prime submodule

Jituparna Goswami

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.

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|ISSN 1686-0209|