Subsocles and direct sum of uniserial modules

Year 2021, Volume: 8 Issue: 3, 213 - 218, 15.09.2021

Ayazul Hasan

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 $M/S$.

Keywords

QTAG-modules, $h$-pure submodules, Socles

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