This errata sheet is organized by which printing of the book you have. The printing can be found by looking at the string of digits 10 9 8. .. at the bottom of the copyright page: the last digit that appears in this decreasing string indicates the printing.
These are notes for a lecture given at Ohio University on June 3, 2006. An important topic in commutative algebra is the Rees algebra of an ideal in a commutative ring. The Rees algebra encodes a lot of information about the ideal and corresponds geometrically to a blow-up. One can represent the Rees algebra as the quotient of a polynomial ring by an ideal.… (More)
Techniques from algebraic geometry and commutative algebra are adopted to establish suucient polynomial conditions for the validity of implicitization by the method of moving quadrics both for rectangular tensor product surfaces of bi-degree (m; n) and for triangular surfaces of total degree n in the absence of base points.
The concept of a µ-basis was introduced in the case of parametrized curves in 1998 and generalized to the case of rational ruled surfaces in 2001. The µ-basis can be used to recover the parametric equation as well as to derive the implicit equation of a rational curve or surface. Furthermore, it can be used for surface reparametrization and computation of… (More)
The Eisenstein irreducibility critierion is part of the training of every mathematician. I first learned the criterion as an undergraduate and, like many before me, was struck by its power and simplicity. This article will describe the unexpectedly rich history of the discovery of the Eisenstein criterion and in particular the role played by Theodor… (More)
1. Gröbner Bases Gröbner bases were introduced in Bucherger's thesis  and developed further in [1, 3]. These methods are now featured in textbooks such [6, 7] and have been implemented in most computer algebra systems. The book  gives a nice survey of where the field was 10 years ago. The basic theory of Gröbner bases includes monomial orders, the… (More)