Some remarks on unilateral matrix equations

We briefly review the results of our paper(4): We study certain perturbativ e solutions of left-unilateral matrix equations. These are algebraic equati ons where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncom mutative algebra, and all coefficients are on the left. Recently such equat ions have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation be tween them are studied, applying a unified approach based on the generalize d Bezout theorem for matrix polynomials.