Some model theory over hereditary Noetherian domains

DOI10.1006/jabr.1998.7607zbMath0942.16003OpenAlexW2067470974MaRDI QIDQ1279823

M. Y. Prest, Gennadi Puninski

Publication date: 6 June 2000

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

Full work available at URL: https://semanticscholar.org/paper/cfbd9bb44678ae9bb1cd2e28c042a0a7ae301de4

zbMATH Keywords

universal enveloping algebrasword problemsimple modulesdirect summandsgeneralized Weyl algebraspure-injective modulesdifferential polynomial ringsZiegler spectraCantor-Bendixson rankshereditary Noetherian domains

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Injective modules, self-injective associative rings (16D50) Undecidability and degrees of sets of sentences (03D35) Rings of differential operators (associative algebraic aspects) (16S32) Other classes of modules and ideals in associative algebras (16D80) Word problems, etc. in computability and recursion theory (03D40) Twisted and skew group rings, crossed products (16S35) Noetherian rings and modules (associative rings and algebras) (16P40) Applications of logic in associative algebras (16B70)

Related Items

Pure injective envelopes of finite length modules over a generalized Weyl algebra, Applications of duality to the pure-injective envelope., Unnamed Item, Triangulated categories and the Ziegler spectrum, Critical and injective modules over skew polynomial rings, WHEN COTORSION MODULES ARE PURE INJECTIVE, Decidability and modules over Bézout domains, Left almost split morphisms and generalized Weyl algebras, Finite length and pure-injective modules over a ring of differential operators, Strongly simply connected algebras with super-decomposable pure-injective modules

Cites Work

• Remarks on elementary duality
• Model theory of modules
• Auslander-Reiten sequences over Artinian rings
• The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
• Auslander-Reiten sequences over derivation polynomial rings
• Ziegler spectra of tame hereditary algebras
• Superdecomposable pure injective modules over commutative valuation rings
• The simple modules of certain generalized crossed products
• Model theory of modules over a serial ring
• Wild torsion modules over Weyl algebras and general torsion modules over HNPs
• Modules over Dedekind prime rings
• Hereditary Noetherian prime rings
• Modules over bounded Dedekind prime rings. II
• Homomorphisms and extensions of modules over certain differential polynomial rings
• Four concepts from “geometrical” stability theory in modules
• Dimension theory for nonsingular injective modules
• Elementary Duality of Modules
• The Ziegler spectrum of a tame hereditary algebra
• The elementary theory of abelian groups
• Bounded Hereditary Noetherian Prime Rings
• Elementary properties of Abelian groups
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