Conditions for a ring to be Noetherian or Artinian

DOI10.1081/AGB-120013181zbMath0998.16006MaRDI QIDQ4532324

Hansuk Tansee, Somyot Plubtieng

Publication date: 21 August 2002

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

zbMATH Keywords

finitely generated modulesdirect sumsdirect summandsNoetherian modulesArtinian modulesextending modules

Mathematics Subject Classification ID

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) Artinian rings and modules (associative rings and algebras) (16P20) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (1)

RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN

Cites Work

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• On rings with restricted minimum condition
• A note on GV-modules with Krull dimension
• All finitely generatedM-subgenerated modules are extending
• A characterization of noetherian rings by cyclic modules
• Rings whose finitely generated modules are extending

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