arXiv subjects

Nazer H. Halimi

Publications and source records attributed to Nazer H. Halimi.

2 recordsLinked to original sources

arXiv2012

Right Mori Orders

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 $ν$-irreducible ideals of the form $aS:_rb$ for some regular $a,b\in S$.

math.RA↗

arXiv2011

Star operation on orders in simple Artinian rings

Star operations are an important tool in multiplicative ideal theory. In this paper we apply a special type of star operation, known as $ν$-operation, to define the notion of right Prüfer $ν$-multiplication order. The latter may be viewed as a natural non-commutative version of Prüfer $ν$-multiplication domain. As one of our main results, we establish that an overring of a right Prüfer $ν$-multiplication order is again a right Prüfer $ν$-multiplication order.

math.RA↗