Modules over crossed products of a division ring by a free Abelian group. I

DOI10.1006/jabr.1999.8194zbMath0958.16028OpenAlexW4210735570MaRDI QIDQ1577618

C. J. B. Brookes, J. R. J. Groves

Publication date: 24 January 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8194

zbMATH Keywords

crossed productspolyhedraGelfand-Kirillov dimensiondivision ringsfree Abelian groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Other classes of modules and ideals in associative algebras (16D80) Twisted and skew group rings, crossed products (16S35)

Related Items (13)

A dichotomy for the Gelfand-Kirillov dimensions of simple modules over simple differential rings ⋮ On the structure of groups admitting faithful modules with certain conditions of primitivity ⋮ Abelian-by-polycyclic groups of homological type FP3 ⋮ MODULES OVER QUANTUM LAURENT POLYNOMIALS ⋮ On a Conjecture of Groves for Modules Over Infinite Nilpotent Groups ⋮ Some infinite soluble groups, their modules, and the arithmeticity of associated automorphism groups. ⋮ Modules over infinite nilpotent groups ⋮ Representations of then-Dimensional Quantum Torus ⋮ Large commutative subalgebras of quantum algebras. ⋮ Homogeneity and rigidity of the Brookes-Groves invariant for the non-commutative torus. ⋮ GK Dimensions of Simple Modules OverK[X^±1, σ] ⋮ Modules over crossed products of a division ring by a free Abelian group. II ⋮ Polyhedrality of the Brookes-Groves invariant for the non-commutative torus.

Cites Work

• Arithmeticity of stabilizers of ideals in group rings
• HNN-extensions of finitely presented soluble groups
• 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
• Infinite Crossed Products and Group-Graded Rings
• A Rigidity Property for the Set of all Characters Induced by Valuations
• Valuations and Finitely Presented Metabelian Groups
• Observations on group rings
• Prime Ideals in Group Rings of Polycyclic Groups
• Modules Over Nilpotent Group Rings
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