Stability in graded rings associated with commutative augmented rings

DOI10.1016/j.jalgebra.2021.07.011zbMath1483.16024arXiv1907.04579OpenAlexW3195894928MaRDI QIDQ2049401

Shan Chang

Publication date: 25 August 2021

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

Full work available at URL: https://arxiv.org/abs/1907.04579

zbMATH Keywords

augmentation idealaugmented ringconsecutive quotient

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Cites Work

• Augmentation quotients for complex representation rings of generalized quaternion groups.
• A basis for augmentation quotients of finite Abelian groups.
• Stable augmentation quotients of Abelian groups
• On finite generation of unit groups of commutative group rings
• The periodicity in the graded ring associated with an integral group ring
• Group rings and their augmentation ideals
• Presenting powers of augmentation ideals and Pfister forms
• Augmentation quotients for Burnside rings of some finite \({p}\)-groups
• Augmentation quotients for complex representation rings of dihedral groups.
• Augmentation quotients for real representation rings of cyclic groups
• Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion Abelian groups.
• Structure of augmentation quotients of finite homocyclic Abelian groups.
• On the Structure of Augmentation Quotient Groups for the Generalized Quaternion Group
• On the structure of the augmentation quotient group for some nonabelian 2-groups
• Augmentation quotients for burnside rings of generalized dihedral groups
• The Structure of Powers of the Augmentation Ideal and Their Quotients for the Burnside Ring of a Generalized Quaternion Group
• On a Problem of Karpilovsky
• Augmentation quotients of some classical groups
• Presenting powers of augmentation ideals of elementary \(p\)-groups
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