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

Hrbek, Michal; Růžička, Pavel

Czech. Math. J. 67, No. 2, 367-377 (2017).

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.

MSC:

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

Keywords:

weak basis; regularly weakly based ring; Dedekind domain; perfect ring

Citations:

Zbl 0721.16009