When is every matrix over a division ring a sum of an idempotent and a nilpotent?

DOI10.1016/J.LAA.2014.02.047zbMath1303.15016OpenAlexW2004283084WikidataQ57787673 ScholiaQ57787673MaRDI QIDQ2448225

Yiqiang Zhou, Tsiu-Kwen Lee, Muhammet Tamer Koşan

Publication date: 30 April 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2014.02.047

zbMATH Keywords

division ringnilpotent matrixidempotent matrixmatrix ringsemilocal ringstrongly regular ringnil-clean matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Endomorphism rings; matrix rings (16S50) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Units, groups of units (associative rings and algebras) (16U60)

Related Items (22)

When is every matrix over a ring the sum of two tripotents? ⋮ Unnamed Item ⋮ Nil 𝒢-cleanness and strongly nil 𝒢-cleanness of rings ⋮ A multiplicative dual of nil-clean rings ⋮ On weakly nil-clean rings. ⋮ Matrices over finite fields as sums of periodic and nilpotent elements ⋮ Matrices over Zhou nil-clean rings ⋮ Rings consisting entirely of certain elements ⋮ On graded nil clean rings ⋮ Unnamed Item ⋮ Nil-clean and strongly nil-clean rings. ⋮ Nil-clean companion matrices ⋮ When is every linear transformation a sum of an idempotent one and a locally nilpotent one? ⋮ Conjugate (nil) clean rings and Köthe’s problem ⋮ Rings over which matrices are sums of idempotent and \(q \)-potent matrices ⋮ Commutative weakly nil clean unital rings. ⋮ A note on commutative nil-clean corners in unital rings ⋮ Unnamed Item ⋮ Rings in which every unit is a sum of a nilpotent and an idempotent ⋮ Rings in which every element is either a sum or a difference of a nilpotent and an idempotent ⋮ Unnamed Item ⋮ Nil-clean group rings

Cites Work

• Diagonalizability of idempotent matrices over noncommutative rings
• Nil-clean matrix rings
• Nil clean rings.

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