Primitive Group Rings and Noetherian Rings of Quotients

DOI10.2307/1999955zbMath0562.16005OpenAlexW4250425685MaRDI QIDQ5187413

C. J. B. Brookes, Kenneth A. Brown

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/1999955

zbMATH Keywords

centreprimitive group ringpartial quotient ringhypercentral groupgeneric flatnessabelian subgroup of infinite rankfinite rank subgroupright noetherian subringstorsionfree subgroupZalesskij's intersection theorems

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generalizations of solvable and nilpotent groups (20F19) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50)

Related Items (6)

Spectra of conjugated ideals in group algebras of abelian groups of finite rank and control theorems ⋮ Some infinite soluble groups, their modules, and the arithmeticity of associated automorphism groups. ⋮ Modules over crossed products of a division ring by a free Abelian group. II ⋮ Primitive irreducible representations of finitely generated nilpotent groups ⋮ Locally nilpotent groups with an intersection property ⋮ On the primitive irreducible representations of finitely generated linear groups of finite rank

Cites Work

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• Primitive group rings of soluble groups
• Polynomial rings over finite dimensional rings
• On the Finiteness of Certain Soluble Groups
• On the Residual Simplicity of Certain Modules
• Prime Ideals in Group Rings of Polycyclic Groups
• The Nullstellensatz for Certain Group Rings
• Rings of Quotients of Group Rings
• Quotient Rings of Group Rings
• Krull dimension

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