A criterion for rings which are locally valuation rings

• Autorzy: Kamran Divaani-Aazar , Mohammad Ali Esmkhani , Massoud Tousi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13F05: Dedekind, Pr\"ufer, Krull and Mori rings and their generalizations
• 13F30: Valuation rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 116
• Numer: 2
• Strony: 153-164

Daty

wydano

2009

Twórcy

autor

Kamran Divaani-Aazar

• Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran
• Institute for Studies, in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran

autor

Mohammad Ali Esmkhani

• Department of Mathematics, Zanjan University, P.O. Box 45195-313, Zanjan, Iran

autor

Massoud Tousi

• Institute for Studies, in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran

Identyfikatory

DOI

10.4064/cm116-2-2