Groebner basis reference request

Question

Someone recommended Eisenbud's Section 15 to me, but I am finding it to be a little too terse. Does anyone know of a fairly self-contained introduction to the topic? I am just now finishing up a graduate level course on ring and field theory, so I am at least familiar with the basic ring theoretic concepts.

Answer 1

For a longer exposition, you could try Cox, Little and O'Shea's book Ideals, Varieties, Algorithms.

This book contains a treatment of Grobner bases and a handful of variations on the Buchberger algorithm as it pertains to affine and projective algebraic geometry, with applications to topics like elimination theory and robotics.

Answer 2

2nd Ideals Varieties, and Algorithms. Cox, Little, and O'Shea's followup Using Algebraic Geometry is also a good reference that includes more advanced topics than IVA, such as Groebner bases for modules over polynomial rings, Groebner fan, and Groebner walks.