Groebner Basis

In this chapter we introduce the notion of Groebner basis for an ideal I in k[x₁,...,x_n] through a nice combination of the “ordered” structure of ideals in k[x₁,...,x_n] and a division algorithm in k[x₁,...,x_n]. We give some applications of Groebner bases to some basic questions in algebraic geometry posed earlier in CH.I §§5-6, CH.II §4 and CH.III §6.