# First Steps

Chapter
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 139)

## Abstract

Invariant theory seeks to determine whether a (mathematical) object can be obtained from some other object by the action of some group. One way to answer this question is to find some functions that map from the class of objects to some field (or more generally some ring). Invariants are functions which take the same value on any two objects which are related by an element of the group. Thus if we can find any invariant which takes different values on two objects, then these two objects cannot be related by an element of the group. Ideally, we hope to find enough invariants to separate all objects which are not related by any group element. This means we want to find a (finite) set of invariants f 1,f 2,…,f r with the property that if two objects are not related by the group action then at least one of these r invariants takes different values on the two objects in question.

## Keywords

Invariant Theory Polynomial Ring Galois Theory Dimensional Vector Space Partial Polarization
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.