n-Clean Rings and Weakly Unit Stable Range Rings

DOI10.1081/AGB-200060531zbMath1080.16027OpenAlexW2088507957MaRDI QIDQ5462868

Tong Wenting, Guangshi Xiao

Publication date: 27 July 2005

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

Full work available at URL: https://doi.org/10.1081/agb-200060531

zbMATH Keywords

idempotentsgroup ringsmatrix ringsclean ringssums of unitsrings of formal power series\(n\)-clean rings\(\Sigma\)-clean ringsweakly unit \(1\)-stable rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Group rings (16S34) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Noncommutative local and semilocal rings, perfect rings (16L30) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Related Items (18)

Topologically boolean and g(x)-clean rings ⋮ On graded nil clean rings ⋮ \(P\)-clean rings. ⋮ Examples of clean commutative group rings. ⋮ A generalization of semiclean rings ⋮ On stable range one property and strongly \(\pi\)-regular rings ⋮ Nil clean rings. ⋮ Semiclean rings and rings of continuous functions. ⋮ \(NR\)-clean rings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On Skew Triangular Matrix Rings ⋮ Stable range one on non-zero divisors ⋮ On Rings Whose Elements are the Sum of a Unit and a Root of a Fixed Polynomial ⋮ Unnamed Item ⋮ Unnamed Item ⋮ n-Clean Rings ⋮ CLEANNESS AND RELATED STRUCTURES IN AMALGAMATED DUPLICATION RINGS

Cites Work

• Krull-Schmidt and cancellation over local rings
• Bass's first stable range condition
• Cancellation of modules and groups and stable range of endomorphism rings
• Stable range one for exchange rings
• Two classes of rings generated by their units
• EXTENSIONS OF CLEAN RINGS
• UNITS, IDEMPOTENTS, AND STABLE RANGE CONDITIONS
• COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT
• Strongly 𝜋-regular rings have stable range one
• Strongly clean rings and fitting's lemma
• Exchange rings, units and idempotents
• Semiclean Rings
• On stable range conditions

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