## “School of Mathematics”

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Paper   IPM / M / 16933
School of Mathematics
Title:   Galois covering of pure-semisimple categories
Author(s):
 1 Shokrollah Salarian 2 Razieh Vahed (Joint with E. Mahdavi)
Status:   To Appear
Journal: Kyoto J. Math.
Supported by:  IPM
Abstract:
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.