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
Classification MSC:  13C05, 13F05, 16L30
DOI:  10.21136/CMJ.2017.0632-15

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Affiliations:   Michal Hrbek, Pavel Růžička, Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic, e-mail:,

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