@article {
author = {Asgari, Sh. and Arabi-Kakavand, M. and Khabazian, H.},
title = {Rings for which every simple module is almost injective},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {42},
number = {1},
pages = {113-127},
year = {2016},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-ring if and only if for every simple R-module S, either S is injective or the injective hull of S is projective of length 2. Right Artinian right almost V-rings and right Noetherian right almost V-rings are characterized. A 2×2 upper triangular matrix ring over R is a right almost V-ring precisely when R is semisimple.},
keywords = {Almost injective modules,$V$-rings,almost $V$-rings},
url = {http://bims.iranjournals.ir/article_747.html},
eprint = {http://bims.iranjournals.ir/article_747_f6b734ed6ae927135539c5e60f93a8b0.pdf}
}