Journal of Prime Research in Mathematics

# Weighted homogeneous polynomials with isomorphic milnor algebras

Imran Ahmed
Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan.

$$^{1}$$Corresponding Author: drimranahmed@ciitlahore.edu.pk.

### Abstract

We recall first some basic facts on weighted homogeneous functions and filtrations in the ring A of formal power series. We introduce next their analogues for weighted homogeneous diffeomorphisms and vector fields. We show that the Milnor algebra is a complete invariant for the classification of weighted homogeneous polynomials with respect to right-equivalence, i.e. change of coordinates in the source and target by diffeomorphism.

#### Keywords:

Milnor algebra, right-equivalence, weighted homogeneous polynomial.