Generic Gröbner bases and Weierstrass bases of homogeneous submodules of graded free modules

For a finitely generated graded module M over a polynomial ring R, there is a special system of its generators associated with a linear filter-regular sequence, which is called a Weierstrass basis. In this paper, we describe first properties of Weierstrass bases keeping in mind their relations with generic Gröbner bases and then give a new proof for their existence, in the case where M is a homogeneous submodule of graded free module over R.