Regularly weakly based modules over right perfect rings and Dedekind domains

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 contains a weak basis.

We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains.

Keywords

• weak basis
• regularly weakly based ring
• Dedekind domain
• perfect ring