Polycyclic group rings and unique factorisation rings

DOI10.1017/S0017089500030676zbMath0822.16025MaRDI QIDQ4306210

Kenneth W. MacKenzie

Publication date: 5 October 1995

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

zbMATH Keywords

maximal ordersprime elementsnormal elementsOre setsprime Noetherian ringsgroup rings of polycyclic-by-finite groupsmultiplication of idealsunique factorisation ringsNoetherian unique factorisation domains

Mathematics Subject Classification ID

Group rings (16S34) Ideals in associative algebras (16D25) Divisibility, noncommutative UFDs (16U30) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Ore rings, multiplicative sets, Ore localization (16U20) Localization and associative Noetherian rings (16P50)

Cites Work

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• Localisation in Asano orders
• Non-commutative unique factorization domains
• Non-commutative UFD's are often PID's
• Height One Primes of Polycyclic Group Rings
• Non-Commutative Unique Factorisation Rings
• Unique factorisation rings
• Quotient Rings of Group Rings

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