6584

6584

زيرمدول هاي اول از مدول هاي آزاد متناهياً توليد شده

كارشناسي ارشد

رياضي محض

مهر1385

مهر1385

دكتر حميد آقا تولايي

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.