TY - JOUR
ID - 747
TI - Rings for which every simple module is almost injective
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Asgari, Sh.
AU - Arabi-Kakavand, M.
AU - Khabazian, H.
AD - Department of Mathematical Sciences, University of Isfahan, Isfahan, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.
AD - Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran.
Y1 - 2016
PY - 2016
VL - 42
IS - 1
SP - 113
EP - 127
KW - Almost injective modules
KW - $V$-rings
KW - almost $V$-rings
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_747.html
L1 - http://bims.iranjournals.ir/article_747_f6b734ed6ae927135539c5e60f93a8b0.pdf
ER -