The Baer-Kaplansky theorem for all abelian groups and modules

5 Jan 2021 Simion Breaz Tomasz Brzeziński

It is shown that the Baer-Kaplansky theorem can be extended to all abelian groups provided that the rings of endomorphisms of groups are replaced by trusses of endomorphisms of corresponding heaps. That is, every abelian group is determined up to isomorphism by its endomorphism truss and every isomorphism between two endomorphism trusses associated to some abelian groups $G$ and $H$ is induced by an isomorphism between $G$ and $H$ and an element from $H$... (read more)

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Categories


  • GROUP THEORY
  • RINGS AND ALGEBRAS
  • 20K30, 16Y99