Linear Algebra in Residue Class Rings

Abstract

The K-vector space structure on residue class rings of polynomial rings has already been used in Section 6.3 in connection with zero-dimensional ideals. An important result was that an ideal I is zero-dimensional if and only if the residue class ring modulo I is finite-dimensional as a K-vector space. In this chapter we discuss a number of important algorithms that use linear algebra in connection with Gröbner bases. The focus is on zero-dimensional ideals.