## Algebra and Logic Seminar

An online session of the Algebra and Logic Seminar will be held on October 22, 2021 (Friday) at 2:00 p.m. (UTC +3). A talk on On Some Special Decompositions of Matrices over Fields and Finite Commutative Rings will be delivered by Peter Danchev. Abstract. In order to find a suitable expression of an arbitrary square matrix over an arbitrary field, we prove that every square matrix over an infinite field is always representable as a sum of a diagonalizable matrix and a square-zero nilpotent matrix. In addition, each 2 x 2 matrix over any field admits such a representation. We also show that, for all natural numbers n > 2, every n x n matrix over a finite field having no less than n [...]