Modules satisfying double chain condition on nonfinitely generated submodules have Krull dimension

Modules Whose Small Submodules Have Krull Dimension

The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

Modules Satisfying the Ascending Chain Condition on Submodules with a Bounded Number of Generators

It is proved that if R is a right and left Noetherian ring then the right R-module RI satisfies the ascending chain condition on n-generated submodules, for every positive integer n. Mathematics Subject Classification (2000): 16P70

Uniformly Generated Submodules of Permutation Modules

This paper is motivated by a link between algebraic proof complexity and the representation theory of the finite symmetric groups. Our perspective leads to a series of non-traditional problems in the representation theory of Sn. Most of our technical results concern the structure of “uniformly” generated submodules of permutation modules. We consider (for example) sequences Wn of submodules of ...

On ℤ4 codes satisfying the chain condition

On Regular Rings Satisfying Weak Chain Condition

In this paper, we shall study regular rings satisfying weak chain condition. As main results, we show that regular rings satisfying weak chain condition are unit-regular, and show that these rings have the unperforation and power cancellation properties for the family of finitely generated projective modules.