Grobner Basis Over Ideals of Multivariate Polynomial Ring

Abstract

Grobner basis are considered one of the modern mathematical tools which has become of interest for the researchers in all fields of mathematics.

Grobner basis are generally polynomials with multiple variables that has certain characteristics.

it's includes two main axis:                                                                           

1- The first axis we have presented the definition of Grobner basis and their properties.

2- The second axis we have studied some applications of Grobner basis, and we give some examples about its.

The goal of these paper is to identify Grobner basis and some algorithms related to how to find them and talked about the most important applications, including: the issue of belonging and the issue of containment, and to reach our goal to follow the analytical and structural approach, we defined these basis and we have many results, The Grosvenor we obtained is not alone in general and to be single, some additional conditions must be set on these basis, and we conclude that Grobner basis have many applications in the solutions of algebraic equations in more than one transformer and in many fields.