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.

Michal Hrbek, Pavel Růžička, Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic, e-mail: hrbmich@gmail.com, ruzicka@karlin.mff.cuni.cz

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

DOI: 10.21136/CMJ.2017.0632-15

Full text available as PDF.


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