Czechoslovak Mathematical Journal, Vol. 67, No. 2, pp. 367-377, 2017
Regularly weakly based modules over right perfect rings and Dedekind domains
Michal Hrbek, Pavel Růžička
Received November 23, 2015. First published March 1, 2017.
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
Affiliations: Michal Hrbek, Pavel Růžička, Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic, e-mail: email@example.com, firstname.lastname@example.org