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Some remarks on equivalences between categories of modules. (English) Zbl 0708.16002
Let R be a ring with identity. Consider every right R-module P as an A-R- bimodule where \(A=END(P_ R)\). Further denote the functors \(- \otimes_{A}P\): Mod-A\(\to Mod\)-R and Hom(P,-): Mod-R\(\to Mod\)-A by \(T_ P\) and \(H_ P\), respectively. Then necessary and sufficient conditions are given for the pair \((T_ P,H_ P)\) to induce an additive category- equivalence between appropriate full subcategories of Mod-A and Mod-R.
Reviewer: P.N.Anh

MSC:
16D90 Module categories in associative algebras
16D20 Bimodules in associative algebras
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