Non-noetherian down-up algebras

DOI10.1080/00927870008827153zbMath0967.16013OpenAlexW2026452279MaRDI QIDQ4519210

Ellen E. Kirkman, James J. Kuzmanovich

Publication date: 30 May 2001

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

Full work available at URL: https://doi.org/10.1080/00927870008827153

zbMATH Keywords

relationsprime algebrasgeneratorsglobal dimensiondown-up algebrasprimitive ringsnon-Noetherian rings

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Prime and semiprime associative rings (16N60) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Combinatorics of partially ordered sets (06A07) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items

Primitive Ideals of Noetherian Down-Up Algebras ⋮ Basic properties of generalized down-up algebras. ⋮ Homogenized Down-Up Algebras ⋮ The group of automorphisms of the Jacobian algebra \(\mathbb A_n\). ⋮ Gelfand–Kirillov dimension of generalized Weyl algebras (In memory of Guenter Rudolf Krause (1941–2015)) ⋮ Isomorphisms of non-Noetherian down-up algebras ⋮ Calabi–Yau properties of nontrivial Noetherian DG down-up algebras ⋮ The algebra of one-sided inverses of a polynomial algebra. ⋮ Fixed subrings of Noetherian graded regular rings. ⋮ PRIMITIVE IDEALS OF NON-NOETHERIAN DOWN-UP ALGEBRAS ⋮ Down–up algebras over a polynomial base ring 𝕂[t₁,…,t_n] ⋮ Down-up algebras and ambiskew polynomial rings ⋮ Down-Up Algebras From Trees ⋮ Projective resolutions of associative algebras and ambiguities.

Cites Work

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• Graded algebras of global dimension 3
• Prime ideals in skew polynomial rings and quantized Weyl algebras
• Down-up algebras
• Quantization of Chern-Simons gauge theory with complex gauge group
• Noetherian down-up algebras
• Primitivity of Noetherian Down-Up Algebras

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