The aim of this paper is to survey noncommutative rings from the viewpoint of multiplicative
ideal theory. The main classes of rings considered are maximal orders, Krull orders (rings) …

The concept of reduced rank has been a useful tool in studying Noetherian rings, orders in
Artinian rings, and rings with Krull dimension. These classes of rings have been …

This volume is a collection of articles concerning topics in multiplicative ideal theory and
factorization theory. While it is not strictly a conference proceedings, most of its papers were …

The viability of the theory of commutative rings is evident from the many papers on the
subject which are published each month. This is not surprising, considering the many …

The aim of the article is to give a characterization of a multiplication commutative ring with
finitely many minimal prime ideals: Each such ring is a finite direct product of rings∏ i= 1 n D …

The last two decades particular interest has been given to noncommutative arithmetical
rings, in particular to noncommutative Krull rings. Several definitions of noncommutative …

In this paper, we study the prime ideal structure of a class of non-commutative polynomial
rings, called Ore extensions or twisted polynomial rings. Let y be an endomorphism of the …

The mathematical object that describes the factorizations of an element a of an arbitrary ring
R is the partially ordered set of all principal right ideals of R that contain aR. We present a …

Let $ R $ be a maximal subring of a ring $ T $. In this paper we study relation between some
important ideals in the ring extension $ R\subseteq T $. In fact, we would like to find some …

The concept of a primary ideal in commutative rings has been extended in several ways to
noncommutative ring theory. Generically these are called generalized primary conditions …