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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-2-7,
author = {Fatemeh Zareh-Khoshchehreh and Kamran Divaani-Aazar},
title = {The existence of relative pure injective envelopes},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {251-264},
zbl = {1286.16004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-2-7}
}
Fatemeh Zareh-Khoshchehreh; Kamran Divaani-Aazar. The existence of relative pure injective envelopes. Colloquium Mathematicae, Tome 131 (2013) pp. 251-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-2-7/