Given a commutative ring A there are different approaches to understand its structure; one is
consider ideals and their arithmetic (multiplicative theory), and another one is to consider …

Given a commutative ring A there are different approaches to understand its structure; one is
consider ideals and their arithmetic (multiplicative theory), and another one is to consider …

One problem in the study of the decomposition of modules is to choose the simple pieces to
build such decompositions. In the noetherian case these simple pieces are the coprimary …

In this paper we introduce the notion of bounded modules and fully bounded modules. A
right R-module M is called a bounded module if every essential submodule of M contains a …

0. Introduction. Let R be a ring. A proper left ideal L of R is prime if, for any elements a and b
in R such that aRb CL, either a€ L or b 6 L. For example, any prime two-sided ideal is a …

The proof of Theorem 1 can be found in [I, Corollaries 17.4 and 18.81 and [7]. The
equivalence of (i) and (v) is Osofsky's Theorem. This is but one of a number of theorems …

This paper is devoted to studying*-Noetherian modules as a new class of Noetherian
modules. A module M is*-Noetherian if Nil (M) is divided prime and each submodule that …

The concept of an eM-Noetherian module is a generalisation of Noetherian and e-
Noetherian modules which is defined as every ascending chain of essential M-cyclic …

For any commutative ring A we introduce a generalization of S--noetherian rings using a
here\-ditary torsion theory σ instead of a multiplicatively closed subset S⊆A. It is proved that …

Here is yet another “non-commutative geometry”. It can be described briefly as follows: take
a commutative noetherian ring R (eg the coordinate ring of an affine variety); describe Spec …