A criterion for rings which are locally valuation
Commutative Algebra
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0702372,
title = {A criterion for rings which are locally valuation},
author = {Kamran Divaani-Aazar and Mohammad Ali Esmkhani and Massoud Tousi},
journal= {arXiv preprint arXiv:math/0702372},
year = {2007}
}
Comments
11 pages