A criterion for rings which are locally valuation rings

Kamran Divaani-Aazar, Mohammad Ali Esmkhani, and Massoud Tousi. "A criterion for rings which are locally valuation rings." Colloquium Mathematicae 116.2 (2009): 153-164. <http://eudml.org/doc/283679>.

@article{KamranDivaani2009,
abstract = {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.},
author = {Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi},
journal = {Colloquium Mathematicae},
keywords = {absolutely pure module; cyclically pure-injective module; projective principal ring; Prüfer domain; semihereditary ring; semisimple ring; valuation ring},
language = {eng},
number = {2},
pages = {153-164},
title = {A criterion for rings which are locally valuation rings},
url = {http://eudml.org/doc/283679},
volume = {116},
year = {2009},
}

TY - JOUR
AU - Kamran Divaani-Aazar
AU - Mohammad Ali Esmkhani
AU - Massoud Tousi
TI - A criterion for rings which are locally valuation rings
JO - Colloquium Mathematicae
PY - 2009
VL - 116
IS - 2
SP - 153
EP - 164
AB - 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.
LA - eng
KW - absolutely pure module; cyclically pure-injective module; projective principal ring; Prüfer domain; semihereditary ring; semisimple ring; valuation ring
UR - http://eudml.org/doc/283679
ER -