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math.GR2021
The Baer-Kaplansky theorem for all abelian groups and modules
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 cor…
math.RA2021
When is every non central-unit a sum of two nilpotents?
Simion Breaz, Yiqiang Zhou
A ring is said to satisfy the -nil-sum property if every non central-unit is the sum of two nilpotents. We prove that a ring satisfies the -nil-sum property iff it is either…