Localization and ideal theory in Noetherian strongly group-graded rings

DOI10.1016/0021-8693(87)90181-5zbMath0607.16013OpenAlexW2005772328MaRDI QIDQ1085252

Allen D. Bell

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90181-5

zbMATH Keywords

prime idealslocalizationNoetherian ringspolycyclic-by-finite groupstrongly G-graded ringfinitely generated uniform right R-moduleprime annihilatorright second layer condition

Mathematics Subject Classification ID

Group rings (16S34) Graded rings and modules (associative rings and algebras) (16W50) 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 (25)

Links between prime ideals in differential operator rings ⋮ The second layer condition for certain centralizing extensions of FBN rings and polynomal rings ⋮ Simple graded rings ⋮ Prime ideals in finite extensions of Noetherian rings ⋮ The influence of ideal structure on representation theory ⋮ Classical Quotient Rings of Group Graded Rings ⋮ Chain conditions for epsilon-strongly graded rings with applications to Leavitt path algebras ⋮ Quotient rings of graded associative rings. I. ⋮ Prime links in some skew-polynomial and skew-laurent rings ⋮ On classical Krull dimension of group-graded rings ⋮ Simple graded rings, nonassociative crossed products and Cayley–Dickson doublings ⋮ Localization in a Morita context with applications to fixed rings ⋮ Localization and Catenarity in Iterated Differential Operator Rings ⋮ Prime ideals in skew polynomial rings and quantized Weyl algebras ⋮ Prime ideals of graded rings and related matters ⋮ Localization in Ore extensions of commutative Noetherian rings ⋮ Catenarity in rings with abelian group action ⋮ A Class of Auslander-Regular Macaulay Rings ⋮ Prime ideals of \(q\)-commutative power series rings. ⋮ Localization and Catenarity in Strongly Graded Rings ⋮ Rings Graded by Polycyclic-by-Finite Groups ⋮ Finite Normalizing Extensions of FSN Rings ⋮ The second layer condition relative to a torsion radical ⋮ Simple semigroup graded rings ⋮ Remarks on the twisted adjoint representation ofR_q[G]

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