The Ladder Construction of Pruefer Modules

TL;DR

This paper introduces a method to construct Pruefer modules over rings using a ladder approach based on specific module homomorphisms, expanding the understanding of their structure.

Contribution

It presents a novel ladder construction technique for Pruefer modules starting from a pair of particular module homomorphisms.

Findings

Provides a new construction method for Pruefer modules

Establishes conditions for the existence of Pruefer modules

Enhances understanding of module endomorphisms

Abstract

Let R be a ring (associative, with 1). A non-zero module M is said to be a Pruefer module provided there exists a surjective, locally nilpotent endomorphism with kernel of finite length. The aim of this note is construct Pruefer modules starting from a pair of module homomorphisms w,v: U_0 -> U_1, where w is injective and its cokernel is of finite length.