On system solvability of non-commutative algebraic equations gerated context -free languages

Systems of algebraic (polynominal) equations under non-commutative one relative to a multiplication ring are considered. The paper considers the solvability condition of such systems as formal power series, systems of linear algebraic equations. The reduction possibility of the system degree was investigated for such equations. The given systems generalize features of equation systems determining context-free and linear languages.