• Corpus ID: 2901166

Ikeda-Nakayama modules.

  title={Ikeda-Nakayama modules.},
  author={Robert Wisbauer and Mohamed Yousif and Yiqiang Zhou},
Let SMR be an (S,R)-bimodule and denote lS(A) = {s ∈ S : sA = 0} for any submodule A of MR. Extending the notion of an Ikeda-Nakayama ring, we investigate the condition lS(A ∩ B) = lS(A) + lS(B) for any submodules A,B of MR. Various characterizations and properties are derived for modules with this property. In particular, for S = End(MR), the π-injective modules are those modules MR for which S = lS(A)+ lS(B) whenever A∩B = 0, and our techniques also lead to some new results on these modules… 
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