Regularly weakly based modules over right perfect rings and Dedekind domains. (English) Zbl 1458.13010

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
(1) rings over which all modules are regularly weakly based, refining results of B. Nashier and W. Nichols [Manuscr. Math. 70, No. 3, 307–310 (1991; Zbl 0721.16009)], and
(2) regularly weakly based modules over Dedekind domains.


13C05 Structure, classification theorems for modules and ideals in commutative rings
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
16L30 Noncommutative local and semilocal rings, perfect rings


Zbl 0721.16009
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