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november 2020 A note on Feigelstock's conjecture on the equivalence of the notions of nil and associative nil groups in the context of additive groups of rings of finite rank
Mateusz Woronowicz
Bull. Belg. Math. Soc. Simon Stevin 27(4): 509-519 (november 2020). DOI: 10.36045/j.bbms.190913

Abstract

In the class of torsion-free abelian groups of finite rank, Feigelstock's conjecture on the equivalence of the notions of nil and associative nil groups is reduced to indecomposable groups. Torsion-free abelian groups $A$ of rank two such that every associative ring on $A$ is commutative but there exists a~non-commutative ring with the additive group $A$, are classified. Moreover, several valuable results concerning rings on torsion-free abelian groups of rank two achieved by Beaumont, Wisner, Jackett, Aghdam and Najafizadeh are complemented and their proof are greatly simplified.$

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Mateusz Woronowicz. "A note on Feigelstock's conjecture on the equivalence of the notions of nil and associative nil groups in the context of additive groups of rings of finite rank." Bull. Belg. Math. Soc. Simon Stevin 27 (4) 509 - 519, november 2020. https://doi.org/10.36045/j.bbms.190913

Information

Published: november 2020
First available in Project Euclid: 20 November 2020

MathSciNet: MR4177390
Digital Object Identifier: 10.36045/j.bbms.190913

Subjects:
Primary: 13A99, 20K15

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 4 • november 2020
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