Primitive Ideals in Group Rings of Polycyclic Groups

Robert L. Snider

doi:10.2307/2040850

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Primitive Ideals in Group Rings of Polycyclic Groups

Robert L. Snider

Year: 1976 Journal: Proceedings of the American Mathematical Society Vol: 57 (1)Pages: 8-8 Publisher: American Mathematical Society

DOI: 10.2307/2040850

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Abstract

If $F$ is a field which is not algebraic over a finite field and $G$ is a polycyclic group, then all primitive ideals of the group ring $F[G]$ are maximal if and only if $G$ is nilpotent-by-finite.

Keywords:

Nilpotent Group ring Mathematics Group (periodic table) Pure mathematics Ring (chemistry) Field (mathematics) Algebraic number Chemistry Algebra over a field Mathematical analysis

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Topics

Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Finite Group Theory Research

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Primitive Ideals in Group Rings of Polycyclic Groups

Abstract

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