\(\aleph_0\)-categoricity and stability of rings

DOI10.1016/0021-8693(77)90359-3zbMath0368.16001OpenAlexW2081275964MaRDI QIDQ1242979

John T. Baldwin, Bruce I. Rose

Publication date: 1977

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

Full work available at URL: https://doi.org/10.1016/0021-8693(77)90359-3

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Model-theoretic algebra (03C60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Other classical first-order model theory (03C68) General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras (16-00)

Related Items (13)

COMPLETENESS AND CATEGORICITY (IN POWER): FORMALIZATION WITHOUT FOUNDATIONALISM ⋮ On \(\omega\)-categorical, generically stable groups and rings ⋮ On \(\omega \)-categorical groups and rings of finite burden ⋮ On \(\aleph_0\)-categorical nilrings ⋮ The periodic power of \(\mathcal A\) and complete Horn theories ⋮ Rings which admit elimination of quantifiers ⋮ Stability theory and Algebra ⋮ Totally categorical groups and rings ⋮ On ℵ₀-categorical nilrings. II ⋮ On relationships between algebraic properties of groups and rings in some model-theoretic contexts ⋮ On 𝜔-categorical groups and rings with NIP ⋮ On the structure of \(\aleph_0\)-categorical groups ⋮ \(\aleph _0\)-categoricity of semigroups

Cites Work

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• On universal Horn classes categorical in some infinite power
• \(\aleph_0\)-categoricity for rings without nilpotent elements and for Boolean structures
• Model theory
• Stable theories
• The number of non-isomorphic models of an unstable first-order theory
• \(\aleph_0\)-categoricity of groups
• Representation of semi-simple algebraic algebras
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• $ℵ_1$ - Kategorische Theorien nicht-kommutativer Ringe
• Categoricity and stability of commutative rings
• Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory
• Categoricity in Power
• Horn sentences
• Topological Representation of Algebras

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