ALGORITHMS FOR SOLVING LINEAR EQUATIONS OVER ASSOCIATIVE RINGS WITH UNIT ELEMENT

摘要

Algorithms are proposed for solving linear equations and systems of such equations in associative noncommutative rings with unit provided that all coefficients in the equations are unit divisors. Basic concepts of the theory of rings and examples of operation of the proposed algorithms are given. The complexity of the algorithms depends on the properties of the elements of the ring over which the equations and systems of equations are considered.