Title of article :
The Dual Notion of Fuzzy Prime Submodules
Author/Authors :
Ansari Toroghy, H University of Guilan , Mahboobi Abkenar. F University of Guilan
Abstract :
Let R be a commutative ring and let M be an R-module. In
this paper, we introduce the dual notion of fuzzy prime (that is, fuzzy
second) submodules of M and explore some of the basic properties of
this class of submodules. We say a non-zero fuzzy submodule µ of M
is fuzzy second if for each r ∈ R, we have 1r.µ = µ or 1r.µ = 1θ . It is shown that the fuzzy second submodules is a proper subclass of the fuzzy coprimary submodules.
Keywords :
Fuzzy submodule , fuzzy second submodule , minimal fuzzy submodule
