TITLE:
Solving Some Problems and Elimination in Systems of Polynomial Equations
AUTHORS:
Moumouni Djassibo Woba
KEYWORDS:
Identity of Bezout, Ring of Bezout, Ideals, Polynomials, Common
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.14 No.3,
September
23,
2024
ABSTRACT: In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime elements in a main ring. A ring that satisfies the property of the theorem is called a Bezout ring. We have given some geometry theorems that can be proved algebraically, although the methods of geometry and, in particular, of projective geometry are by far the most beautiful. Most geometric problems actually involve polynomial equations and can be translated into the language of polynomial ideals. We have given a few examples of a different nature without pretending to make a general theory.