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A criterion for rings which are locally valuation

Kamran Divaani-Aazar·Mohammad Ali Esmkhani·Massoud Tousi
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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.

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Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi. 2007-02-13. A criterion for rings which are locally valuation. https://arxiv.org/abs/math/0702372

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