The theory of Gröbner bases
The aim of this paper is the study of Gröbner bases which are finite ideal bases, such that the initial terms of them generate the ideal generated by all initial terms of polynomials of the given ideal. Such bases are characterized based on a generalization of a usual division algorithm of univariate polynomials (see also Bayer, Buchberger 1985). A construction of a Gröbner basis from a given finite ideal basis is explained (see also Kandry-Rody and Kapru 1984) and the method of Gröbner basis is applied to a geometric problem: to obtain the Zariski- closure in the projective n-space of an algebraic subset of affine n- space. The work contains the ``algebraic'' results about Gröbner bases but no results about complexity of corresponding algorithms.
scientific article; zbMATH DE number 4150360