Regular submodules of torsion modules over a discrete valuation domain

TL;DR

This paper establishes necessary and sufficient conditions for the regularity of submodules within p-primary modules of bounded order over a discrete valuation domain, enhancing understanding of their structural properties.

Contribution

It provides a complete characterization of regular submodules in p-primary modules over a discrete valuation domain, which was previously not fully understood.

Findings

Derived necessary and sufficient conditions for regularity

Connected regularity to the existence of simultaneous bases

Improved structural understanding of submodules in p-primary modules

Abstract

A submodule $W$ of a p-primary module $M$ of bounded order is known to be regular if $W$ and $M$ have simultaneous bases. In this paper we derive necessary and sufficient conditions for regularity of a submodule.