Abstract
This is the second part of the paper with the same title published in Communications in Algebra in 2011. It contains applications of the Latticial Osofsky–Smith Theorem to Grothendieck categories and module categories equipped with a torsion theory. Various many different meanings spread in the literature of the relative concepts with respect to a hereditary torsion theory τ on Mod-R like τ-essential submodule, τ-complement submodule, τ-CS module, etc. are also discussed.
ACKNOWLEDGMENTS
The author thanks N. V. Dung for drawing to his attention the paper Dung [Citation19], Constantin Năstăsescu and John Van Den Berg for helpful discussions, Septimiu Crivei for providing him references [Citation13, Citation14, Citation16], and the referee for his/her careful reading of the manuscript and helpful suggestions.
Notes
Communicated by J. L. Gomez Pardo.