Zero divisors and units with small supports in group algebras of torsion-free groups

DOI10.1080/00927872.2017.1344688zbMath1425.20005arXiv1705.00152OpenAlexW2963942145MaRDI QIDQ4643675

Alireza Abdollahi, Zahra Taheri

Publication date: 28 May 2018

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.00152

zbMATH Keywords

group ringzero divisortorsion-free groupdivisor graphKaplansky's unit conjectureKaplansky's zero divisor conjecturezero unit graph

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Units, groups of units (associative rings and algebras) (16U60)

Related Items

Unit groups of finite group algebras of abelian groups of order 17 to 20 ⋮ Cardinality of product sets in torsion-free groups and applications in group algebras ⋮ Zero divisor and unit elements with supports of size 4 in group algebras of torsion-free groups ⋮ Zero divisors of support size 3 in group algebras and trinomials divided by irreducible polynomials over GF(2)

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• The zero divisor question for supersolvable groups

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