Editing Ring theory (section)

===Ring of invariants===
A basic (and perhaps the most fundamental) question in the classical [[invariant theory]] is to find and study polynomials in the polynomial ring <math>k[V]</math> that are invariant under the action of a finite group (or more generally reductive) ''G'' on ''V''. The main example is the [[ring of symmetric functions|ring of symmetric polynomials]]: [[symmetric polynomial]]s are polynomials that are invariant under permutation of variable. The [[fundamental theorem of symmetric polynomials]] states that this ring is <math>R[\sigma_1, \ldots, \sigma_n]</math> where <math>\sigma_i</math> are elementary symmetric polynomials.