On the axiomatizability of certain classes of modules

DOI10.1007/BF01174803zbMath0387.03012OpenAlexW2061412990MaRDI QIDQ1250211

Christian U. Jensen, Peter Vámos

Publication date: 1979

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/172850

zbMATH Keywords

DIMENSION THEORYFINITE AXIOMATIZABILITYFIRST ORDER LANGUAGE OF MODULES OVFLAT MODULEINJECTIVE MODULENOETHERIAN RINGREPRESENTATIONS

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Projectives and injectives (category-theoretic aspects) (18G05) Foundations of classical theories (including reverse mathematics) (03B30) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Representation theory of associative rings and algebras (16Gxx)

Related Items

Modules, Ideals and modules testing injectivity, Extensions of elementary duality

Cites Work

• Every two elementarily equivalent models have isomorphic ultrapowers
• Direct Products of Modules
• Definability problems for modules and rings
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