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A characterization of Prüfer rings. (English) Zbl 0539.13009

The main result is the following: A domain R is a Prüfer domain if and only if for every R-module M of finite type, the torsion submodule \(\tau\) (M) is a pure submodule. As a corollary one gets the theorem of I. Kaplansky [J. Indian Math. Soc., New Ser. 24, 279-281 (1961; Zbl 0118.272)] that R is Prüfer iff for every R-module M of finite type \(\tau\) (M) is a direct summand.
Reviewer: N.Sankaran

MSC:

13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations

Citations:

Zbl 0118.272