On FI-cotorsion modules and dimensions
Abstract
In this paper we study the class of FI-cotorsion modules and we introduce there dimensions of modules and rings. An R-module M is called FI-cotorsion if Ext1R(F,M) = 0 for any FI-flat R-module F. Also, we investigate some properties of FI-cotorsion modules and FI-cotorsion envelopes and we give a characterization of IF-ring. Then, we study the FI-flat and the FI-cotorsion envelope and we show when they existed. Furthermore, we present the notation of FI-cotorsion dimension of modules and rings.
Copyright © 2021 Afaf Dhafer Alqahtani, Khalid Ouarghi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
A. D. Alqahtani, K. Ouarghi, On FI-cotorsion modules and dimensions, J. Math. Comput. Sci. 11 (2021), 6980–6998. https://doi.org/10.28919/jmcs/6453
BibTeX
@article{Alqahtani2021,
author = {Alqahtani, Afaf Dhafer and Ouarghi, Khalid},
title = {On FI-cotorsion modules and dimensions},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {6980--6998},
doi = {10.28919/jmcs/6453}
}