Some ∗-Clean Group Rings

DOI10.1142/S1005386715000152zbMath1316.16018MaRDI QIDQ5496368

Yanyan Gao, Yuan Lin Li, Jian-Long Chen

Publication date: 30 January 2015

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

zbMATH Keywords

unitsprojectionsidempotentsgroup ringsunit groupsclean ringsrings with involution\(*\)-clean rings

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Units, groups of units (associative rings and algebras) (16U60)

Related Items (11)

Idempotents of generalized quaternion group algebras and their applications ⋮ $\ast$-Semiclean rings ⋮ On nil clean group rings ⋮ On *-Clean Group Rings II ⋮ On \(\ast\)-clean group rings over finite fields ⋮ Clean group rings over localizations of rings of integers ⋮ On *-clean non-commutative group rings ⋮ On ∗-clean group rings over abelian groups ⋮ ∗-Cleanness of finite group rings ⋮ Strongly 2-nil-clean rings with involutions ⋮ New \(\ast\)-clean finite group rings under the conjugate involution

Cites Work

• \(*\)-clean rings; some clean and almost clean Baer \(*\)-rings and von Neumann algebras.
• Group rings in which every element is uniquely the sum of a unit and an idempotent.
• Rings in which elements are uniquely the sum of an idempotent and a unit that commute.
• EXTENSIONS OF CLEAN RINGS
• ON STRONGLY *-CLEAN RINGS
• Local Group Rings
• Some Results on Semi-Perfect Group Rings

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