Abstract

DANCHEV, Peter V.. Certain Properties of Square Matrices over Fields with Applications to Rings. Rev.colomb.mat. [online]. 2020, vol.54, n.2, pp.109-116.  Epub Mar 04, 2021. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v54n2.93833.

We prove that any square nilpotent matrix over a field is a difference of two idempotent matrices as well as that any square matrix over an algebraically closed field is a sum of a nilpotent square-zero matrix and a diagonalizable matrix. We further apply these two assertions to a variation of π-regular rings. These results somewhat improve on establishments due to Breaz from Linear Algebra & Appl. (2018) and Abyzov from Siberian Math. J. (2019) as well as they also refine two recent achievements due to the present author, published in Vest. St. Petersburg Univ. - Ser. Math., Mech. & Astr. (2019) and Chebyshevskii Sb. (2019), respectively.

Keywords : Nilpotent matrices; idempotent matrices; Jordan canonical form; algebraically closed fields; super π-regular rings.

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