On the Properties of Rings of Integro-Differential Operators and Their Corresponding Equations

The paper deals with systems of linear integro-differential equations, including systems with a matrix identically degenerate in the domain at the highest derivative of the unknown vector function. A theorem on the solvability of such systems of equations is proved. On the basis of this theorem, it is shown that the ring of operators corresponding to these systems contains the semigroup of operators for which a left inverse operator from this ring is found.