Michal Hrbek, Pavel Růžička, Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic, e-mail: firstname.lastname@example.org, email@example.com
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
Classification (MSC 2010): 13C05, 13F05, 16L30
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