Radikal formülünü sağlayan modüller

ABSTRACT ON MODULES WHICH SATISFY THE RADICAL FORMULA Kılıçarslan, Sibel Master, Department of Mathematics Supervisor: Associated Prof. Dilek Pusat Yılmaz June 2004, 80 pages Let R be a commutative ring with identity and M be an i?-module. M satisfies the radical formula if for every submodule N of M, the radical of N is the submodule generated by its envelope. Prime submodules should be studied before we examine the radical formula. So definition of prime submodule and some characterizations of prime submodules are given in chapter I. In chapter II, we discussed under what conditions prime radical of a module is distributive over intersection. In chapter III, envelope of a module is introduced and modules which satisfy the radical formula are investigated. In last chapter, generalization of Cohen's theorem, which gives the relationship between a Noetherian ring and prime ideals, to modules is given and we discussed ascending chain condition on modules. Keywords: Prime submodule, prime radical, radical formula. 11