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A criterion for rings which are locally valuation rings

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Divaani-Aazar K., Esmkhani M., Tousi M.

Colloquium Mathematicum

2009

tom 116

nr 2

153-164

Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer 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 semisimple if and only if every R-module is cyclically pure injective.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Divaani-Aazar K.

1 Esmkhani M.

1 Tousi M.

1 2009

Wyniki wyszukiwania

A criterion for rings which are locally valuation rings