We wrote this book to introduce undergraduates to some interesting ideas in algebraic
geometry and commutative algebra. For a long time, these topics involved a lot of abstract …

In nice cases, a zero-dimensional complete intersection ideal over a field has a Shape
Lemma. There are also cases where the ideal is generated by the resultant and first …

This paper presents an innovative algebraic sensor fault detection approach for surge
avoidance in turbo compressors (TC) in the natural gas compressor stations (GCS). The …

In Chapter 1, we have seen how the algebra of the polynomial rings k [x 1,…, xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

Invariant theory has had a profound effect on the development of algebraic geometry. For
example, the Hilbert Basis Theorem and Hilbert Nullstellensatz, which play a central role in …

This chapter will introduce some of the basic themes of the book. The geometry we are
interested in concerns affine varieties, which are curves and surfaces (and higher …

In this chapter we will consider two applications of concepts and techniques from algebraic
geometry in areas of computer science. First, continuing a theme introduced in several …

In § 10 of Chapter 2 we discussed some criteria designed to identify situations where it is
possible to see in advance that an S-polynomial remainder will be zero in Buchberger's …

The most important invariant of a linear subspace of affine space is its dimension. For affine
varieties, we have seen numerous examples which have a clearly defined dimension, at …

So far all of the varieties we have studied have been subsets of affine space kn. In this
chapter, we will enlarge kn by adding certain “points at∞” to create n-dimensional projective …