TY  - JOUR
TI  - Semisimple-direct-injective modules
AB  - The notion of simple-direct-injective modules which are a generalization of injective modules unifies$C2$ and $C3$-modules. In the present paper,we introduce the notion of the semisimple-direct-injective module which gives a unified viewpoint of $C2$, $C3$, SSP properties and simple-direct-injective modules.It is proved that a ring $R$ is Artinian serial with the Jacobson radical square zero if and only if every semisimple-direct-injective right $R$-module has the SSP and, for any family of simple injective right $R$-modules ${S_i}_{mathcal{I}}$, $oplus_{mathcal{I}}S_i$ is injective. We also show that$R$ is a right Noetherian right V-ring if and only if every right $R$-module has a semisimple-direct-injective envelope if and only if every right $R$-module has a semisimple-direct-injective cover.
AU  - CONG QUYNH, TRUONG
AU  - Kosan, Tamer
AU  - Abyzov, Adel
AU  - Tapkin, Dan
DO  - 10.15672/hujms.730907
PY  - 2021
JO  - Hacettepe Journal of Mathematics and Statistics
VL  - 50
IS  - 2
SN  - 1303-5010
SP  - 516
EP  - 525
DB  - TRDizin
UR  - http://search/yayin/detay/492884
ER  -