The principal ideal theorem in prime Noetherian rings

DOI10.1017/S0017089500006340zbMath0579.16001OpenAlexW2142039790MaRDI QIDQ3701576

Martin Philip Gilchrist, A. W. Chatters

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1017/s0017089500006340

zbMATH Keywords

prime idealmaximal ordersfully bounded noetherian ringelements regular modulo aheight-1 primesprime noetherian rings

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (1)

On noncommutative bounded factorization domains and prime rings

Cites Work

• Maximal orders in Artinian rings
• Prime ideals in PI-rings
• Reduced rank in Noetherian rings
• The Poincaré series of the ring of 2x2 generic matrices
• Principal ideal theorem for Noetherian P.I.rings
• Stable structure of noncommutative Noetherian rings
• Jacobson's conjecture and modules over fully bounded Noetherian rings
• Idealizers and hereditary Noetherian prime rings
• Krull and Global Dimensions of Semiprime Noetherian PI-Rings
• Relative krull dimension and prime ideals in right noetherian rings
• Artinian Quotient Rings^†
• Localization and the AR Property

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