Topologically semisimple and topologically perfect topological rings

11 Mar 2020 Positselski Leonid Stovicek Jan

Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category of left contramodules over such a ring is split (equivalently, semisimple) if and only if the abelian category of discrete right modules over the same ring is split (equivalently, semisimple). Our results in this direction complement those of Iovanov-Mesyan-Reyes... (read more)

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Categories


  • CATEGORY THEORY
  • RINGS AND ALGEBRAS