
Chapter 7
Commutative Gröbner Bases
7.1 Introduction
The final chapters of this book provide an introduction to the well-known
theory of commutative Gröbner bases, which has many applications through-
out the mathematical sciences. After much discussion, we made the somewhat
unexpected decision to put these chapters at the end of the book, for the fol-
lowing reasons. First, as we mentioned previously, there is a natural logical
progression from noncommutative Gröbner bases to Gröbner bases for op-
erads, which cannot be extended backward to include commutative Gröbner
bases.
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Second, we are interested in commutative Gröbner bases almost exclu-
sively