Noter olmayan bazı bölgeler

Let R be a commutative ring and M be an R-module. We say that M satisfiesthe radical formula (s.t.r.f.) if for every submodule N of M, radical of N in M isequal to the envelope of N inM. Since the Noetherian rings which s.t.r.f. are wellknown,see [9],[13],[17],[19],[20], we are interested in non-Noetherian rings whichs.t.r.f. For this reason we studied characteristics and structure of a valuation ringto understand the structure of a Pr¨ufer domain. In chapter I, basic definitions andfundamental facts related to the concept of valuation rings and Pr¨ufer domainsare presented.In Chapter II, we solved some selected exercises in [7] about valuation ringsand Pr¨ufer domains.In Chapter III, we gave necessary definitions and characterizations of primesubmodules.Finally, the definitions and fundamental results about radical formula aregiven in chapter IV. In 4.2, which is our original work, we proved that if R is aPrüfer domain, then the R module the direct sum of R by itself s.t.r.f.