GENERATING IDEALS IN COMMUTATIVE ARTINIAN GROUP RINGS AND A GENERALIZE D PASCAL'S TRIANGLE

DOI10.1081/AGB-120015674zbMath1042.13011OpenAlexW2081012407MaRDI QIDQ4796315

David E. Rush, J. S. Okon

Publication date: 2002

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

Full work available at URL: https://doi.org/10.1081/agb-120015674

zbMATH Keywords

minimal number of generatorsPascal's triangleDilworth numberSperner numberArtin local ringprincipal local 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) Regular local rings (13H05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The upper bound of the Dilworth number and the Rees number of Noetherian local rings with a Hilbert function
• Rings with two-generated ideals
• Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras
• The Dilworth number of Artin Gorenstein rings
• On the number of generators of ideals in local rings
• Two-generated ideals and representations of Abelian groups over valuation rings
• Two-generated ideals in non-Noetherian semigroup rings
• Numbers of generators of ideals in a group ring of an elementary Abelian \(p\)-group
• An integer-valued function related to the number of generators of modules over local rings of small dimension
• Group rings with n-generated ideals
• Commutative Semigroup Rings with Two-Generated Ideals
• On generators of ideals in one-dimensional local rings
• Bounding the number of generators for a class of ideals in local rings
• Numbers of generators of ideals in zero-dimensional group rings
• A Gorenstein Ring with Larger Dilworth Number than Sperner Number
• The dilworth number of group rings over an artin local ring
• Three results on the number of generators of ideals
• The Number of Generators of Some Homogeneous Ideals
• Group rings R[G with 3-generated ideals when R is artinian]

This page was built for publication: GENERATING IDEALS IN COMMUTATIVE ARTINIAN GROUP RINGS AND A GENERALIZE D PASCAL'S TRIANGLE