A note on Noetherian orders in Artinian rings

DOI10.1017/S0017089500003827zbMath0405.16002OpenAlexW2126024895MaRDI QIDQ4190769

A. W. Chatters

Publication date: 1979

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0017089500003827

zbMATH Keywords

Nilpotent RadicalRegular ElementsArtinian IdealCentral IdempotentDecomposition Theorem for Left and Right Noetherian P.P. RingsLeft and Right Noetherian Ring Which Has An Artinian Quotient Ring

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Conditions on elements (16U99) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Artinian rings and modules (associative rings and algebras) (16P20) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Modules, bimodules and ideals in associative algebras (16Dxx) Radicals and radical properties of associative rings (16Nxx)

Related Items (2)

Decomposition of orders in semiprimary rings ⋮ Modules

Cites Work

• Orders in Artinian rings
• Orders in Artinian rings. II
• Shorter Notes: Artinian Ideals in Noetherian Rings
• Two results on p.p. rings
• A Decomposition Theorem for Noetherian orders in Artinian Rings
• HEREDITARY RINGS
• AN EXAMPLE IN NOETHERIAN RINGS
• On some questions in Noetherian rings
• Semihereditary rings

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