Right Mori Orders

Abstract

In this paper we study \textit{right Mori Orders}, which are those prime Goldie rings that satisfy the ascending chain condition on regular integral right divisorial right ideals. We will show that the class of right Mori orders is closed with respect to Morita-equivalence. We also prove that each regular right divisorial right ideal of a right Mori order is contained in only finitely many right divisorial completely prime right ideals. Moreover, we show that such right divisorial ideals can be represent as a finite intersection of $\nu$-irreducible ideals of the form $aS:_rb$ for some regular $a,b\in S$.