Abstract: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 Rmodule has the SSP and, for any family of simple injective right R-modu… Show more
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