ABSTRACT

"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."

chapter Chapter I|32 pages

Affine Algebraic Sets and the Nullstellensatz

chapter Chapter II|35 pages

Polynomial and Rational Functions

chapter Chapter III|42 pages

Projective Algebraic Sets

chapter Chapter IV|36 pages

Groebner Basis

chapter Chapter V|60 pages

Dimension of Algebraic Sets

chapter Chapter VI|45 pages

An Introduction to Local Theory

chapter Chapter VII|53 pages

Curves

chapter Chapter VIII|35 pages

Elliptic Curves