The Cohen type theorem and the Eakin-Nagata type theorem for \(S\)-Noetherian rings revisited

DOI10.1216/RMJ.2020.50.619zbMath1440.13016OpenAlexW3030188792MaRDI QIDQ2188455

Jung Wook Lim, Dong Kyu Kim

Publication date: 11 June 2020

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1590739294

zbMATH Keywords

\(S\)-Noetherian module(right) \(S\)-Noetherian ringCohen type theoremEakin-Nagata type theorem

Mathematics Subject Classification ID

Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras (16P99) Ideals and multiplicative ideal theory in commutative rings (13A15) Ideals in associative algebras (16D25) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (6)

ALMOST MULTIPLICATIVE SETS ⋮ A Cohen-type theorem for w-Noetherian modules ⋮ \(S\)-injective modules ⋮ Eakin-Nagata-Eisenbud theorem for right \(S\)-Noetherian rings ⋮ Unnamed Item ⋮ THE S-FINITENESS ON QUOTIENT RINGS OF A POLYNOMIAL RING

Cites Work

• Unnamed Item
• Unnamed Item
• \(S\)-Noetherian properties on amalgamated algebras along an ideal
• \(s\)-Noetherian rings and their extensions
• Chain conditions on composite Hurwitz series rings
• The converse to a well known theorem on Noetherian rings
• A type of subrings of a noetherian ring
• Commutative rings with restricted minimum condition
• A Note on S-Noetherian Domains
• S-NOETHERIAN RINGS
• Agreeable domains
• S-Noetherian Properties of Composite Ring Extensions

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