# Algebraic geometry and commutative algebra, 7.5 ECTS

Second level## Facts

No available facts## Description

The course covers rings, ideals, prime ideals, nilpotency, zero divisors, modules, Noetherian rings, Hilbert’s basis theorem, finite extensions and Noetherian normalization, Nullstellensatz, Spec, rings of quotients, primary decomposition. Algebraic geometry is the study of solutions of systems of polynomial equations. Commutative algebra is the basic algebraic tool. The course is an introduction to these fields. One example of application is coding theory.

## Area of interests: Information only in Swedish

## Subject

### Mathematics

As a mathematical theory always implies that certain conclusions hold under certain given conditions, it can in principle say nothing about the physical reality. None the less mathematics has become an indispensable tool for a large number of subjects like astronomy, physics, chemistry, statistics and the technical sciences and in later times also for economy, biology, various social sciences and computor science. The role of mathematics in the applied sciences is both to supply notions for exact and adequate formulations of empirical laws but also from these laws to derive consequences, which can be used to find better models of the reality one has to describe. These tasks have lately become more important. Mathematics is in continual progress by intensive international research, new theories are created and already existing theories are simplified and augmented.