Abstract
The paper contains the complete classification of nil rings with decomposable torsion-free additive group of rank two and description of nil rings with indecomposable torsion-free additive group of rank two. Moreover, it is shown that an indecomposable non-nil torsion-free abelian group $A$ of rank two supports only nilpotent rings exactly if $A$ is the additive group of a nil ring. Some decomposition criteria for torsion-free abelian groups of rank two are also included.
Citation
Ryszard R. Andruszkiewicz. Mateusz Woronowicz. "On the Classification of Torsion-Free Nil Rings of Rank Two." Bull. Belg. Math. Soc. Simon Stevin 30 (2) 176 - 193, september 2023. https://doi.org/10.36045/j.bbms.221123
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