On group rings of nilpotent groups

DOI10.1007/BF02761167zbMath0556.16006MaRDI QIDQ761528

Leonid G. Makar-Limanov

Publication date: 1984

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

zbMATH Keywords

group algebrasskew fields of fractionsOre domainsfree subalgebratorsion-free non-abelian nilpotent group

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Group rings (16S34) Nilpotent groups (20F18) Localization and associative Noetherian rings (16P50) Division rings and semisimple Artin rings (16Kxx)

Related Items (13)

Free algebras and free groups in Ore extensions and free group algebras in division rings. ⋮ A Survey on Free Objects in Division Rings and in Division Rings with an Involution ⋮ Free algebras in division rings with an involution ⋮ Generalised Tits alternative for linear semigroups ⋮ Obtaining free group algebras in division rings generated by group graded rings ⋮ Free group algebras in division rings with valuation I ⋮ On free group algebras in division rings with uncountable center ⋮ Free Group Algebras in Division Rings with Valuation II ⋮ Free subalgebras of division algebras over uncountable fields. ⋮ On free subgroups in division rings ⋮ Free products of units in algebras. I: Quaternion algebras ⋮ Free Fields in Malcev–Neumann Series Rings ⋮ A commutativity theorem for division rings and an extension of a result of Faith

Cites Work

• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• The skew field of fractions of the weyl algebra contains a free noncommutative subalgebra
• Quotient Rings of Group Rings
• The Group Ring Of a Class Of Infinite Nilpotent Groups
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