Group rings in which every element is uniquely the sum of a unit and an idempotent.

DOI10.1016/j.jalgebra.2006.08.012zbMath1110.16025OpenAlexW2057579366MaRDI QIDQ858717

Yiqiang Zhou, W. Keith Nicholson, Jian-Long Chen

Publication date: 11 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.08.012

zbMATH Keywords

unitsidempotentsgroup ringsuniquely clean rings

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Units, groups of units (associative rings and algebras) (16U60)

Related Items (26)

Uniquely exchange rings ⋮ Cleanness of the Group Ring of an Abelian p-Group over a Commutative Ring ⋮ Characterizations of special clean elements and applications ⋮ Nil-clean and strongly nil-clean rings. ⋮ Rings whose clean elements are uniquely clean ⋮ Idempotent operator and its applications in Schur complements on Hilbert \(C^*\)-module ⋮ A CLASS OF EXCHANGE RINGS ⋮ On feckly polar rings ⋮ Some new characterizations of periodic rings ⋮ J-Boolean group rings and skew group rings ⋮ A Class of Quasipolar Rings ⋮ Rings in which elements are uniquely the sum of an idempotent and a unit that commute. ⋮ On *-Clean Group Rings II ⋮ On \(\ast\)-clean group rings over finite fields ⋮ On Uniquely Clean Rings ⋮ Expressing infinite matrices as sums of idempotents ⋮ Group rings that are UJ rings ⋮ Some ∗-Clean Group Rings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On *-clean group rings ⋮ A survey of strongly clean rings. ⋮ ON STRONGLY *-CLEAN RINGS ⋮ On Quasipolar Rings ⋮ Exchange Ideals with All Idempotents Central ⋮ Strongly \(P\)-clean and semi-Boolean group rings

Cites Work

• Continuous modules are clean.
• Strong finiteness conditions in locally finite groups
• Clean general rings.
• EXTENSIONS OF CLEAN RINGS
• A CHARACTERIZATION OF UNIT REGULAR RINGS
• Lifting Idempotents and Exchange Rings
• Observations on group rings
• Exchange rings, units and idempotents
• RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT
• Local Group Rings
• On the Group Ring

This page was built for publication: Group rings in which every element is uniquely the sum of a unit and an idempotent.