Commentaries on Hilbert’s Basis Theorem

Abstract

The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert’s basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert’s theorem to examine their unique properties which will help us to understand some of the characteristics of the Noetherian rings.