"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."
"This book can be used as a first course in algebraic geometry for students and researchers who are not primarily pure mathematicians. It is also useful for applications in computer algebra, robotics and computational geometry and mathematical methods in technology. … I wish to recommend this well-written book to anyone interested in applied algebraic geometry."
- EMS Newsletter, June 2003
Affine algebraic sets and the Nullstellensatz; polynomial and rational functions; projective algebraic sets; Groebner basis; dimension of algebraic sets; an introduction to local theory; curves; elliptic curves. Appendices: finiteness conditions and field extensions; localization, discrete valuation rings and Dedekind domains.