Dedekind Asal Halkalar ve Genelleştirmeleri

Abstract

The commutative theory of Dedekind domains is well developed in literature and much isknown about the arithmetic of ideals and also the structure of modules over a Dedekinddomain. There have been many studies on the generalization of the commutative idea ofa Dedekind domain to noncommutative rings. The aim of this thesis is to investigate theclass of rings which arose from this idea of generalization namely; Dedekind prime rings,Asano right orders, hereditary rings and G-Dedekind prime rings and to investigate thelocalization problem on the ring of Asano right orders.