A ring/~ is said to be invariant or a duo-ring ifaR= Ra holds for all a in R. If a RCR a or R a C
a/~ holds for all a in R, then we say R is semi-invariant. In this paper we will be concerned …

1. Introduction. An element a of a ring 9Î is said to be regular if there exists an element x of dt
such that axa= a. A ring 9î with unit element, every element of which is regular, is a regular …

In ring theory there is the following theorem (cf.[1], p. 39): If R is a ring satisfying the
descending chain condition for left ideals, then the following three conditions are …

Let Q be a (Noetherian) local ring with maximal ideal m, and let p be a prime ideal in Q such
that dim p+ rank p= dim Q. Serre showed, using homological means, that if Q is regular, then …

An equiprime near-ring is a generalization of prime ring. Firstly some axioma-tics concerning
equiprime near-rings are discussed, eg their relation to the other notions of primeness for …

Introduction Throughout this paper, every ring is assumed to have an identity. The main
theme of the paper is the investigation of rings in which finitely generated right ideals are …

Completely prime ideals have been studied for associative rings by Andrtmakievic and
Rjabuhin in [2] and also by McCoy in [5]. The purpose of this note is to extend these results …

The main result of this paper is the explicit determination of the core of integrally closed
ideals in 2-dimensional regular local rings. The core of an ideal I in a ring R was introduced …

Generalizing results of Joseph and Small, we show that if B is a Noetherian ring and A a
Noetherian subring, and P is a prime ideal of B, then there is a certain set X of primes in A …

Der Dedekindsche Differentensatz der algebraischen Zahlentheorie besagt bekanntlich: In
der (Dedekindschen) Differente der Hauptordnung R eines endlichen algebraischen …