Group rings \(R[G]\) with \(4\)-generated ideals when \(R\) is an Artinian principal ideal ring (Q2785908)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Group rings \(R[G]\) with \(4\)-generated ideals when \(R\) is an Artinian principal ideal ring |
scientific article; zbMATH DE number 983051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Group rings \(R[G]\) with \(4\)-generated ideals when \(R\) is an Artinian principal ideal ring |
scientific article; zbMATH DE number 983051 |
Statements
24 April 1997
0 references
4-generated ideals
0 references
Artinian principal ideal rings
0 references
finite Abelian groups
0 references
group rings
0 references
0 references
0 references
0.84165746
0 references
Group rings \(R[G]\) with \(4\)-generated ideals when \(R\) is an Artinian principal ideal ring (English)
0 references
Let \(R\) be a commutative Artinian principal ideal ring and let \(G\) be a finite abelian group. The purpose of this paper is to give necessary and sufficient conditions for the group ring \(RG\) to have the property that all its ideals can be generated by at most 4 elements. (The case of 3 generators has been treated in [\textit{S. Ameziane Hassani}, \textit{M. Fontana} and \textit{S. Kabbaj}, Commun. Algebra 24, No. 4, 1253-1280 (1996; Zbl 0849.16025)].) The result, which is much too long to state here, follows after a substantial number of long case-by-case calculations.NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].
0 references
