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- W2023596287 abstract "A module M over a ring is called simple-direct-injective if, whenever A and B are simple submodules of M with A≅B and B⊆⊕M, we have A⊆⊕M. Various basic properties of these modules are proved, and some well-studied rings are characterized using simple-direct-injective modules. For instance, it is proved that a ring R is artinian serial with Jacobson radical square zero if and only if every simple-direct-injective right R-module is a C3-module, and that a regular ring R is a right V-ring (i.e., every simple right R-module is injective) if and only if every cyclic right R-module is simple-direct-injective. The latter is a new answer to Fisher's question of when regular rings are V-rings [8]." @default.
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- W2023596287 date "2014-12-01" @default.
- W2023596287 modified "2023-09-30" @default.
- W2023596287 title "Simple-direct-injective modules" @default.
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- W2023596287 doi "https://doi.org/10.1016/j.jalgebra.2014.07.033" @default.
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