%0 Journal Article
%T Rings for which every simple module is almost injective
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Asgari, Sh.
%A Arabi-Kakavand, M.
%A Khabazian, H.
%D 2016
%\ 02/01/2016
%V 42
%N 1
%P 113-127
%! Rings for which every simple module is almost injective
%K Almost injective modules
%K $V$-rings
%K almost $V$-rings
%R
%X 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.
%U http://bims.iranjournals.ir/article_747_f6b734ed6ae927135539c5e60f93a8b0.pdf