Subsocles and direct sum of uniserial modules

Abstract

Suppose $M$ is a QTAG-module with a subsocle $S$ such that $M/S$ is a direct sum of uniserial modules. Our global aim here is to investigate an interesting connection between the structure of $M/S$ and the QTAG-module $M$. Specifically, the condition $S = Soc(N)$ for some $h$-pure submodules $N$ of $M$ allows $M$ to inherit the structure of $M/S$.

Received: 27 November 2020 | Accepted: 16 April 2021