1
Department of Mathematical Sciences, University of Isfahan, Isfahan, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.
2
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran.
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.
Asgari, S., Arabi-Kakavand, M., & Khabazian, H. (2016). Rings for which every simple module is almost injective. Bulletin of the Iranian Mathematical Society, 42(1), 113-127.
MLA
Asgari, S., Arabi-Kakavand, M., & Khabazian, H. "Rings for which every simple module is almost injective", Bulletin of the Iranian Mathematical Society, 42, 1, 2016, 113-127.
HARVARD
Asgari S., Arabi-Kakavand M., Khabazian H. (2016). 'Rings for which every simple module is almost injective', Bulletin of the Iranian Mathematical Society, 42(1), pp. 113-127.
CHICAGO
S. Asgari, M. Arabi-Kakavand & H. Khabazian, "Rings for which every simple module is almost injective," Bulletin of the Iranian Mathematical Society, 42 1 (2016): 113-127,
VANCOUVER
Asgari S., Arabi-Kakavand M., Khabazian H. Rings for which every simple module is almost injective. BIMS. 2016;42(1):113-127.
