Regularly weakly based modules over right perfect rings and Dedekind domains

summary: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 \endgraf (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and \endgraf (2) regularly weakly based modules over Dedekind domains