A criterion for rings which are locally valuation

Divaani-Aazar, Kamran; Esmkhani, Mohammad Ali; Tousi, Massoud

A criterion for rings which are locally valuation

Authors

Divaani-Aazar, Kamran

Esmkhani, Mohammad Ali

Tousi, Massoud

Description

Using the notion of cyclically pure injective modules, a characterization for rings which are locally valuation is established. As applications, new characterizations for Prufer domains and pure semi-simple rings are provided. Namely, we show that a domain R is Prufer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semi-simple if and only if every R-module is cyclically pure injective.
11 pages