On a theorem of kulikov for artinian rings

DOI10.1080/00927878208822726zbMath0484.16016OpenAlexW1968507492MaRDI QIDQ3943095

Hermann Brune

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1080/00927878208822726

zbMATH Keywords

global dimensionfinite representation typealmost split sequencepure-projective modulesdirect sum of finitely presented modulesright artinian ringindecomposable injective right modulesdirect sum of finitely generated modulesKulikov propertylocally noetherian functor categories

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Homological dimension in associative algebras (16E10) Artinian rings and modules (associative rings and algebras) (16P20) Representation theory of associative rings and algebras (16Gxx)

Related Items

Separable modules over finite-dimensional algebras, Auslander-Reiten sequences over Artinian rings, Strong preinjective partitions and almost split morphisms, Infinite dimensional serial algebras and their representations, A homological approach to representations of algebras. II: Tame hereditary algebras, On the global dimension of the functor category \(((\bmod R)^{op},Ab)\) and a theorem of Kulikov

Cites Work

• Direct sums and direct products of canonical pencils of matrices
• On the difference between cohomological dimension and homological dimension
• Purity in functor categories
• Rings with several objects
• Some left pure semisimple ringoids which are not right pure semisimple
• Representation Theory of Artin Algebras II
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