Algebraic conditions for the solvability of system of three linear equations in a ring.

In this paper, we give algebraic conditions for the existence of a solution and the expression for the general solution of the system of the equations a 1 x b 1 = c 1 , a 2 x b 2 = c 2 , a 3 x b 3 = c 3 , when each element belongs to a ring with a unit. As an application, we get necessary and sufficient conditions for the existence of common inner inverse of three regular elements. [ABSTRACT FROM AUTHOR]