On division rings generated by polycyclic groups

DOI10.1007/BF02760514zbMath0533.20016OpenAlexW2046479062MaRDI QIDQ789509

Bertram Arthur Frederick Wehrfritz

Publication date: 1984

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02760514

zbMATH Keywords

group of unitssubgroup of finite indexArtin-Rees propertydivision ring generated by polycyclic-by-finite subgroup of multiplicative groupfinitely generated skew linear groupsfinitely generated subringideal of finite indexplinthsresidually a finite p-groupring of matrices

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Solvable groups, supersolvable groups (20F16) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generators, relations, and presentations of groups (20F05) Other matrix groups over rings (20H25) Residual properties and generalizations; residually finite groups (20E26) Units, groups of units (associative rings and algebras) (16U60) Division rings and semisimple Artin rings (16Kxx) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (2)

On PI-subrings of matrix rings over some classes of skew fields ⋮ Trace Functions in the Ring of Fractions of Polycyclic Group Rings

Cites Work

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• On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group
• Integral group rings of polycyclic-by-finite groups
• On linear groups over a field of fractions of a polycyclic group ring
• Group rings of polycyclic groups
• Remarks on centrality and cyclicity in linear groups
• On Abelian-By-Polycyclic Groups
• Prime Ideals in Group Rings of Polycyclic Groups
• A Note on the Artin-Rees Property of certain Polycyclic Group Algebras
• The Units of Group-Rings

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