Connected graded Gorenstein algebras with enough normal elements

DOI10.1006/jabr.1996.6885zbMath0937.16049OpenAlexW2087070452MaRDI QIDQ1355591

James J. Zhang

Publication date: 4 June 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1996.6885

zbMATH Keywords

quantum algebrasmaximal ordersglobal dimensionsinjective dimensionsconnected graded algebrasgraded prime idealsenough normal elementsgraded Noetherian algebrashomogeneous normal elementsquasi-Frobenius quotient rings

Mathematics Subject Classification ID

Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Growth rate, Gelfand-Kirillov dimension (16P90) Graded rings and modules (associative rings and algebras) (16W50) Homological dimension in associative algebras (16E10) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (35)

Frobenius-Perron theory for projective schemes ⋮ Non-commutative Castelnuovo-Mumford regularity and AS-regular algebras. ⋮ The Nakayama automorphism of a class of graded algebras ⋮ Homological properties of quantized coordinate rings of semisimple groups ⋮ On the trace of graded automorphisms ⋮ Quantum graded algebras with a straightening law and the AS-Cohen-Macaulay property for quantum determinantal rings and quantum Grassmannians. ⋮ RING THEORETIC PROPERTIES OF QUANTUM GRASSMANNIANS ⋮ Sklyanin algebras and Hilbert schemes of points ⋮ Catenarity in quantum algebras ⋮ Weighted homological regularities ⋮ Auslander theorem for PI Artin-Schelter regular algebras ⋮ A class of AS-regular algebras of dimension five. ⋮ Noncommutative cyclic isolated singularities ⋮ Growth of graded noetherian rings ⋮ Gorensteinness of invariant subrings of quantum algebras ⋮ Rigidity of graded regular algebras ⋮ Auslander’s Theorem for permutation actions on noncommutative algebras ⋮ The AS-Cohen-Macaulay property for quantum flag manifolds of minuscule weight ⋮ Some properties of the extremal algebras. ⋮ Double Ore extensions. ⋮ Dualizing Complexes of Noetherian Complete Algebras via Coalgebras ⋮ HOMOGENEOUS PBW DEFORMATION FOR ARTIN–SCHELTER REGULAR ALGEBRAS ⋮ Homological identities for noncommutative rings ⋮ Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity ⋮ QUANTUM ANALOGUES OF SCHUBERT VARIETIES IN THE GRASSMANNIAN ⋮ Noncommutative Auslander theorem ⋮ Asymmetry of Ext-groups ⋮ Gorenstein homomorphisms of noncommutative rings ⋮ Gourmet's guide to Gorensteinness ⋮ Rings with Auslander dualizing complexes ⋮ Pertinency of Hopf actions and quotient categories of Cohen-Macaulay algebras ⋮ Properties of AS-Cohen-Macaulay algebras ⋮ Intersection multiplicity over noncommutative algebras ⋮ Noncommutative complete intersections ⋮ Gorenstein Dimension and AS-Gorenstein Algebras

Cites Work

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• Graded algebras of global dimension 3
• Modules over regular algebras of dimension 3
• Dualizing complexes over noncommutative graded algebras
• Homological properties of (graded) Noetherian PI rings
• Noncommutative projective schemes
• Catenarity in quantum algebras
• Injective dimension of semi-primary rings
• Some properties of non-commutative regular graded rings
• Auslander-Regular Algebras and Maximal Orders
• Serre duality for noncommutative projective schemes
• Growth of graded noetherian rings

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