# Regularly weakly based modules over right perfect rings and Dedekind domains

## TL;DR

This paper investigates the properties of regularly weakly based modules over specific rings, including right perfect rings and Dedekind domains, refining existing theoretical results in module theory.

## Contribution

It characterizes rings where all modules are regularly weakly based and analyzes such modules over Dedekind domains, advancing the understanding of module generation properties.

## Key findings

- Identifies rings where all modules are regularly weakly based.
- Provides a detailed study of regularly weakly based modules over Dedekind domains.
- Refines previous results by Nashier and Nichols.

## Abstract

A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contain a weak basis. In the paper we study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, (2) regularly weakly based modules over Dedekind domains.