Artinian modules and modules of which all proper submodules are finitely generated

DOI10.1016/0021-8693(85)90101-2zbMath0588.13015OpenAlexW1990496574MaRDI QIDQ1073102

David C. Lantz, William J. Heinzer

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0021-8693(85)90101-2

zbMATH Keywords

Artinian modulefinitely generated submodulesminimal infinitely generated modulesquasilocal ring

Mathematics Subject Classification ID

Commutative rings and modules of finite generation or presentation; number of generators (13E15) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Local rings and semilocal rings (13H99)

Related Items

On modules with DICC ⋮ Jónsson extensions of one-dimensional semilocal domains ⋮ α-Noetherian and artinian modules ⋮ Jonsson and HS modules over commutative rings ⋮ SOME ASPECTS OF MODULAR LATTICES WITH DUAL KRULL DIMENSION ⋮ Jónsson Modules over Noetherian Rings ⋮ On Artinian Modules Over Duo Rings ⋮ Rings with finite top ⋮ Dimension and attached primes of an Artinian module ⋮ Modules whose distinct submodules are not isomorphic

Cites Work

• Modules whose proper submodules are finitely generated
• Injective modules over Noetherian rings
• N-rings and ACC on colon ideals
• Loewy and Artinian modules over commutative rings
• Ideals contracted from a Noetherian extension ring
• The Krull intersection theorem. II
• 1-dimensional Cohen-Macaulay rings
• Universally contracted ideals in commutative rings
• Loewy series of modules.
• Rings with an almost Noetherian ring of fractions.
• Modules whose distinct submodules are not isomorphic
• Cardinality of generating sets for modules over a commutative ring.
• The Dual of the Notion of “Finitely Generated”
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