Recently, Zharkov and Blinkov introduced the notion of involutive bases of polynomial ideals. This involutive approach has its origin in the theory of partial differential equations and is a translation of results of Janet and Pommaret. In this paper we present a pure algebraic foundation of involutive bases of Pommaret type. In fact, they turn out to be generalized left Gröbner bases of ideals in the commutative polynomial ring with respect to a non-commutative grading. The introduced theory will allow not only the verification of the results of Zharkov and Blinkov but it will also provide some new facts.