On expressing matrices over \(\mathbb{Z}_2\) as the sum of an idempotent and a nilpotent
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Publication:1638006
DOI10.1016/j.laa.2018.01.015zbMath1482.15027OpenAlexW2793102648MaRDI QIDQ1638006
Publication date: 12 June 2018
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2018.01.015
Matrices over special rings (quaternions, finite fields, etc.) (15B33) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)
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When is every matrix over a ring the sum of two tripotents? ⋮ Decompositions of matrices into diagonalizable and square-zero matrices ⋮ Decompositions of matrices into potent and square-zero matrices ⋮ Nil 𝒢-cleanness and strongly nil 𝒢-cleanness of rings ⋮ Unnamed Item ⋮ On Some Decompositions of Matrices over Algebraically Closed and Finite Fields ⋮ Matrices over finite fields as sums of periodic and nilpotent elements ⋮ Nonderogatory matrices as sums of idempotent and nilpotent matrices ⋮ Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence ⋮ A symmetric generalization of \(\pi\)-regular rings ⋮ Some new characterizations of periodic rings ⋮ Rings over which matrices are sums of idempotent and \(q \)-potent matrices ⋮ On nil clean group rings ⋮ A note on nil-clean rings ⋮ Nil-clean index of \(M_n(\mathbb{F}_2)\) ⋮ Ideally nil clean rings ⋮ A generalization of -regular rings ⋮ \(n\)-torsion clean and almost \(n\)-torsion clean matrix rings ⋮ On the idempotent and nilpotent sum numbers of matrices over certain indecomposable rings and related concepts ⋮ Unnamed Item ⋮ Certain Properties of Square Matrices over Fields with Applications to Rings ⋮ The ring \(\operatorname{M}_{8 k + 4}(\mathbb{Z}_2)\) is nil-clean of index four ⋮ When is a matrix a sum of involutions or tripotents?
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