• 제목/요약/키워드: Left (Right) simple-direct-injective ring

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Some Results on Simple-Direct-Injective Modules

  • Derya Keskin Tutuncu;Rachid Tribak
    • Kyungpook Mathematical Journal
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    • 제63권4호
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    • pp.521-537
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    • 2023
  • 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.