Non-commutative Noetherian Unique Factorization Domains often have stable range one

DOI10.1017/S030500410007804XzbMath0737.16013OpenAlexW2153643250MaRDI QIDQ3982599

Martin Philip Gilchrist

Publication date: 26 June 1992

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s030500410007804x

zbMATH Keywords

enveloping algebrastable rangefinite-dimensional Lie algebraNoetherian integral domainpartial quotient ringintersection conditionheight-1 prime idealNoetherian U.F.D.

Mathematics Subject Classification ID

Ideals in associative algebras (16D25) Divisibility, noncommutative UFDs (16U30) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Integral domains (associative rings and algebras) (16U10)

Cites Work

• Cancellation of modules and groups and stable range of endomorphism rings
• Idealizers and hereditary Noetherian prime rings
• Non-commutative unique factorization domains
• Non-commutative UFD's are often PID's
• Injective modules and classical localization in Noetherian rings
• The divisor function at consecutive integers

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