چكيده
Abstract
This thesis contains four chapters . In the first chapter we give the basic
definitions and theorems of the theory of commutative rings . In the second
chapter we study the properties of prime submodules of R- modules, in
particular we study prime submodules of free modules and also the modules on
some special rings. In the chapter three the cyclic 1-generated submodules of
(n ) F = R
have been studied. In this chapter, an finite m-generated
submodules of
(n ) F = R
,with cyclic prime submodules will be surveyed .In
the last chapter we study 2-generated submodules of
(n ) F = R
which is a
generalization of the 1-generated case . Finally , our aim of this thesis Is to
characterize the prime submodules of finitely generated free modules over
commutative domains in some special cases.
