AN INTERCONECTION BETWEEN A DEDEKIND PRIME RING AND AN HNP RING - (NIM : 20110015), MAHMUDI
This thesis deals with the characterization of a Dedekind prime ring which related to hereditary Noetherian prime (HNP) ring. A Dedekind prime ring can be viewed as a generalization of a Dedekind domain. It is shown that a ring R is Dedekind if only if R is an HNP ring. The above property is generalized to an arbitrary ring, included a noncommutative ring. It is also shown that a ring R is a Dedekind prime ring if only if R is an HNP ring and is a maximal order. This result is the main theorem in this thesis.