Abstract

The aim of this work was to generalize
generator, $M$-generated modules in order to apply them to a wider
class of rings and modules. We started by establishing a new concept
which is called a fully-$M$-cyclic module. We defined this notation
by using $Hom_R(M,*)$ operators which are helpful to contract the
new construction and describe their properties. Finally, we could
see the structure of fully-$M$-cyclic module and quasi-fully-cyclic
module by the structure of $M$.

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