The existence of relative pure injective envelopes

Fatemeh Zareh-Khoshchehreh, and Kamran Divaani-Aazar. "The existence of relative pure injective envelopes." Colloquium Mathematicae 130.2 (2013): 251-264. <http://eudml.org/doc/284110>.

@article{FatemehZareh2013,
abstract = {Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.},
author = {Fatemeh Zareh-Khoshchehreh, Kamran Divaani-Aazar},
journal = {Colloquium Mathematicae},
keywords = {finitely presented modules; pure injective modules; pure injective envelopes; preenveloping classes; left global pure projective dimension; enveloping classes; cyclically presented modules; left global pure injective dimension},
language = {eng},
number = {2},
pages = {251-264},
title = {The existence of relative pure injective envelopes},
url = {http://eudml.org/doc/284110},
volume = {130},
year = {2013},
}

TY - JOUR
AU - Fatemeh Zareh-Khoshchehreh
AU - Kamran Divaani-Aazar
TI - The existence of relative pure injective envelopes
JO - Colloquium Mathematicae
PY - 2013
VL - 130
IS - 2
SP - 251
EP - 264
AB - Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.
LA - eng
KW - finitely presented modules; pure injective modules; pure injective envelopes; preenveloping classes; left global pure projective dimension; enveloping classes; cyclically presented modules; left global pure injective dimension
UR - http://eudml.org/doc/284110
ER -