Some Results on Simple-Direct-Injective Modules
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A module M is called a simple-direct-injective module if, whenever A and B are simple submodules of M with A∼=B and B is a direct summand of M, then A is a direct summand of M. Some new characterizations of these modules are proved. The structure of simple-direct-injective modules over a commutative Dedekind domain is fully determined. Also, some relevant counterexamples are indicated to show that a left simple direct-injective ring need not be right simple-direct-injective.
Abstract
A module M is called a simple-direct-injective module if, whenever A and B are simple submodules of M with A∼=B and B is a direct summand of M, then A is a direct summand of M. Some new characterizations of these modules are proved. The structure of simple-direct-injective modules over a commutative Dedekind domain is fully determined. Also, some relevant counterexamples are indicated to show that a left simple direct-injective ring need not be right simple-direct-injective.
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