Generalized Bassian Modules over Non-primitive Dedekind Prime Rings

TL;DR

This paper characterizes singular generalized bassian modules over non-primitive Dedekind prime rings, expanding understanding of module theory in this algebraic context.

Contribution

It provides a description of singular generalized bassian modules specifically over non-primitive Dedekind prime rings, a novel focus in module theory.

Findings

Characterization of singular generalized bassian modules

Description of modules over non-primitive Dedekind prime rings

Advancement in algebraic module classification

Abstract

A right $A$-module $M$ is said to be generalized bassian if the existence of an injective homomorphism $M\to M/N$ for some submodule $N$ of $M$ implies that $N$ is a direct summand of $M$. We describe singular generalized bassian modules over non-primitive Dedekind prime rings.\\ The study is supported by grant of Russian Science Foundation.