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Paper   IPM / M / 16933
School of Mathematics
  Title:   Galois covering of pure-semisimple categories
1.  Shokrollah Salarian
2.  Razieh Vahed (Joint with E. Mahdavi)
  Status:   To Appear
  Journal: Kyoto J. Math.
  Supported by:  IPM
Let \CC be a locally bounded \k-category, where \k is a field. It is proved that \CC is pure-semisimple, i.e., every object of \Mod \CC is pure-projective, if and only if every family of morphisms between indecomposable finitely generated \CC-modules is noetherian. Our formalism establishes the pure-semisimplicity of Galois coverings, that is, if \CC is a G-category with a free G-action on \ind \CC, then \CC is pure-semisimple if and only if \CC/G is so.

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