Grobner bases and involutive bases

Recently, constructive methods became widely used in the commutative algebra. These methods are mainly based on the theory of Grobner bases and involutive bases. Due to various applications, the investigations of effectiveness of the constructions of the Grobner bases became very timely. The algorithm of constructing the Grobner bases is based on the consideration of S-polynomials and application of a normal simplificator. Usually in order to refine the algorithm of the construction of the Grobner bases, one uses a more elaborate choice of S-polynomials. The effect of the normal simplificator on the effectiveness of the construction of the Grobner bases has been so far studied insufficiently. In this paper we try to establish a relation beta een the theory of Grobner bases and the theory of involutive bases. It is known that any involutive basis contains as a subset the Grobner basis of an ideal. We associate with any Grodner basis with a fixed normal simplificator an involutive basis. Thus, we emphasize the dependence of the effectiveness of a construction of the Grobner basis on the normal simplificator chosen. An attempt has been fulfilled to describe the normal simplificators corresponding to the involutive bases.