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On feebly nil-clean rings

Marjan Sheibani Abdolyousefi;  Neda Pouyan — 2024

Czechoslovak Mathematical Journal

A ring R is feebly nil-clean if for any a ∈ R there exist two orthogonal idempotents e , f ∈ R and a nilpotent w ∈ R such that a = e - f + w . Let R be a 2-primal feebly nil-clean ring. We prove that every matrix ring over R is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.

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