Generalized Rees rings and relative maximal orders satisfying polynomial identities

DOI10.1016/0021-8693(83)90227-2zbMath0521.16003OpenAlexW2022214979MaRDI QIDQ1055516

Freddy M. J. van Oystaeyen, Lieven Le Bruyn

Publication date: 1983

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90227-2

zbMATH Keywords

crossed productsmaximal ordersKrull domains2-cocyclesimple artinian ringarithmetical subringAsano orderDedekind ordergeneralized Rees ringHNP ringnoncommutative Krull ordertame order

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Graded rings and modules (associative rings and algebras) (16W50) Divisibility, noncommutative UFDs (16U30) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Localization and associative Noetherian rings (16P50) Rings with polynomial identity (16Rxx)

Related Items (18)

Ore-Rees rings which are maximal orders. ⋮ Divisorially graded rings, related groups, and sequences ⋮ Krull dimensions of divisorially graded rings ⋮ On bounded v-hc orders in a simple artinian ring ⋮ Arithmetically graded rings revisited ⋮ Non commutative unique factorization rings ⋮ Unnamed Item ⋮ The ramification divisor of regular tame orders,i ⋮ Dehomogenization of Gradings to Zariskian Filtrations and Applications to Invertible Ideals ⋮ ON Ω–KRMULL RINGS ⋮ Some constructions of rings ⋮ What is an \(\Omega\)-Krull ring? ⋮ Class groups of maximal orders over Krull domains ⋮ The Jespers-Van Oystaeyen conjecture ⋮ Generalized crossed products applied to maximal orders, Brauer groups and related exact sequences ⋮ \(\Omega\)-Krull rings and Gr-\(\Omega\)-Krull rings in the non-P.I. case ⋮ On Clifford systems and generalized crossed products ⋮ Graded Dedekind rings

Cites Work

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• Hereditary Prime P.I. Rings are Classical Hereditary Orders†
• Asano Orders
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• On the Picard group of a Grothendieck category

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