Group rings with n-generated ideals

DOI10.1080/00927879208824338zbMath0746.16020OpenAlexW2170200428MaRDI QIDQ3988698

J. S. Okon, J. Paul Vicknair

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1080/00927879208824338

zbMATH Keywords

group ringArtinian ring\(n\)-generator property

Mathematics Subject Classification ID

Group rings (16S34) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Ideals in associative algebras (16D25) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Artinian rings and modules (associative rings and algebras) (16P20)

Related Items

GENERATING IDEALS IN COMMUTATIVE ARTINIAN GROUP RINGS AND A GENERALIZE D PASCAL'S TRIANGLE ⋮ Two-generated ideals in non-Noetherian semigroup rings ⋮ Group rings R[G with 3-generated ideals when R is artinian] ⋮ Numbers of generators of ideals in a group ring of an elementary Abelian \(p\)-group ⋮ Numbers of generators of ideals in zero-dimensional group rings ⋮ The dilworth number of group rings over an artin local ring

Cites Work

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• Local rings with bounded ideals
• Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras
• On the two generator problem for the ideals of a one-dimensional ring
• On the number of generators of ideals in local rings
• On the ubiquity of Gorenstein rings
• Commutative rings with restricted minimum condition
• Torsion-Free Abelian Semigroup Rings, V
• n-Generator Property of a Polynomial Ring
• Arithmetical Semigroup Rings
• Commutative Artinian Principal Ideal Rings

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