GROUP RINGS OF COUNTABLE NON-ABELIAN LOCALLY FREE GROUPS ARE PRIMITIVE

DOI10.1142/S0218196711006273zbMath1228.16020arXiv1010.4898OpenAlexW2962764211MaRDI QIDQ3006613

Tsunekazu Nishinaka

Publication date: 20 June 2011

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4898

zbMATH Keywords

ascending HNN-extensionsprimitive group ringslocally free groups

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Free nonabelian groups (20E05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Local properties of groups (20E25)

Related Items (2)

Uncountable locally free groups and their group rings ⋮ Non-Noetherian groups and primitivity of their group algebras

Cites Work

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• Group rings of proper ascending HNN extensions of countably infinite free groups are primitive.
• Primitive group rings
• Group rings of free products are primitive
• ASCENDING HNN EXTENSIONS OF FINITELY GENERATED FREE GROUPS ARE HOPFIAN
• The Coefficient Ring of a Primitive Group Ring

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