Universal fields of fractions for polycyclic group algebras

DOI10.1017/S0017089500004869zbMath0486.16004MaRDI QIDQ3946284

Donald S.Passman

Publication date: 1982

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

crossed productsAR-propertygroup algebralocalizationpolycyclic-by-finite groupcompletely prime idealclassical ring of quotientsFC-centreuniversal field of fractionsleft Ore setpoly- infinite cyclic group

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (12)

Free subgroups in linear groups over some skew fields ⋮ A Survey on Free Objects in Division Rings and in Division Rings with an Involution ⋮ On PI-subrings of matrix rings over some classes of skew fields ⋮ Free unit groups in group rings and division rings: My collaboration with Don Passman ⋮ Homology growth, hyperbolization, and fibering ⋮ Multipartite rational functions ⋮ On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group ⋮ The soluble subgroups and the Tits alternative in linear groups over rings of fractions of polycyclic group rings. I ⋮ Free subgroups in division rings generated by group rings of soluble groups ⋮ Trace Functions in the Ring of Fractions of Polycyclic Group Rings ⋮ On free subsemigroups of associative algebras ⋮ The universality of Hughes-free division rings

Cites Work

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• Localization in non-noetherian group rings
• Prime Ideals in Group Rings of Polycyclic Groups
• A Note on the Artin-Rees Property of certain Polycyclic Group Algebras
• Localization and the AR Property

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