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Danchev, Peter García, Esther Gómez-Lozano, Miguel Ángel 2025-12-11T12:24:29Z 2025-12-11T12:24:29Z 2025 https://journals.uwyo.edu/index.php/ela/article/view/9099 https://hdl.handle.net/10630/41065 https://doi.org/10.13001/ela.2025.9099 We study the problem of when a periodic square matrix of order n×n over an arbitrary field F is decomposable into the sum of a square-zero matrix and a torsion matrix and show that this decomposition can always be obtained for matrices of rank at least n/2 when F is either a field of prime characteristic, or the field of rational numbers, or an algebraically closed field of zero characteristic. We also provide a counterexample to such a decomposition when F equals the field of the real numbers. eng open access Matrices (Matemáticas) Grupos nilpotentes Decompositions of periodic matrices into a sum of special matrices journal article