Prime affine algebras of Gelfand-Kirillov dimension one

DOI10.1016/0021-8693(84)90110-8zbMath0545.16011OpenAlexW2041457859MaRDI QIDQ797666

Lance W. Small, Robert B. jun. Warfield

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0021-8693(84)90110-8

zbMATH Keywords

centerGelfand-Kirillov dimensionfully bounded noetherianprime finitely generated algebrasimple noetherian algebra

Mathematics Subject Classification ID

Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (45)

Classification of affine prime regular Hopf algebras of GK-dimension one. ⋮ On the codimension sequence of \(G\)-simple algebras. ⋮ Modules over the 4-dimensional Sklyanin algebra ⋮ Survey on Hopf algebras of GK-dimension 1 and 2 ⋮ Division algebras of Gelfand-Kirillov transcendence degree 2. ⋮ Invariants of domains with finite GK dimension. ⋮ On structure of domains with quadratic growth. ⋮ On associative conformal algebras of linear growth. II. ⋮ Noncommutative graded domains with quadratic growth ⋮ Jacobson radical algebras with Gelfand-Kirillov dimension two over countable fields. ⋮ An upper bound for the length of a finite-dimensional algebra ⋮ Leavitt path algebras of hypergraphs ⋮ Golod-Shafarevich algebras, free subalgebras and Noetherian images. ⋮ GK DIMENSION AND LOCALLY NILPOTENT SKEW DERIVATIONS ⋮ Gelfand-Kirillov dimension for rings ⋮ Crossed products and their central polynomials. ⋮ Some noncommutative minimal surfaces ⋮ A Morita Cancellation Problem ⋮ Noncommutative cyclic isolated singularities ⋮ On noncommutative bounded factorization domains and prime rings ⋮ Jacobson radical non-nil algebras of Gel'fand-Kirillov dimension 2. ⋮ 𝐴_{∞}-structures associated with pairs of 1-spherical objects and noncommutative orders over curves ⋮ Noncommutative curves and noncommutative surfaces ⋮ Noncommutative deformations of Kleinian singularities ⋮ Examples in Finite Gel'fand–Kirillov Dimension. II ⋮ Semiprime graded algebras of dimension two ⋮ The prime spectrum of algebras of quadratic growth. ⋮ The Artin-Stafford gap theorem ⋮ Associative conformal algebras of linear growth. ⋮ There are no graded domains with GK dimension strictly between 2 and 3. ⋮ Affine algebras of Gelfand-Kirillov dimension one are PI ⋮ Centers in domains with quadratic growth. ⋮ Associative conformal algebras with finite faithful representation. ⋮ Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin, and Heinzer ⋮ A dichotomy result for prime algebras of Gelfand-Kirillov dimension two. ⋮ Primitivity of finitely presented monomial algebras. ⋮ \(q\)-analogs of harmonic oscillators and related rings ⋮ Examples in finite Gel'fand-Kirillov dimension ⋮ Zariski cancellation problem for non-domain noncommutative algebras ⋮ Primitive algebras with arbitrary Gelfand-Kirillov dimension ⋮ Noetherian connected graded algebras of global dimension 3 ⋮ Simple associative conformal algebras of linear growth ⋮ Locally finite representations over Noetherian Hopf algebras ⋮ Chains of prime ideals and primitivity of \(\mathbb Z\)-graded algebras. ⋮ Algebras which are nearly finite dimensional and their identities

Cites Work

• Representations of solvable Lie algebras. V: On the Gelfand-Kirillov dimension of simple modules
• Transcendental division algebras and simple Noetherian rings
• The Goldie conditions for Algebras with Bounded Growth
• On the Krull-Akizuki Theorem
• Unnamed Item
• Unnamed Item

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