Generic Gröbner bases and Weierstrass bases of homogeneous submodules of graded free modules (Q1582725)

Let \(R=k[x_1, \dots, x_r]\) be a polynomial ring over an infinite field \(k\), and let \(E\) be a finitely generated, homogeneous submodule of arbitrary rank of a graded free \(R\)-module. This paper contains a new proof that there exists a generic Gröbner basis of \(E\) with respect to reverse lexicographic order with ``term over position'', which is also a Weierstrass basis for \(E\). It uses the structure theorem of finitely generated modules over a principal ideal domain. The existence of a Weierstrass basis for \(E\) was proven earlier by the author.