Conjugate Systems of quadratic equations and connection to the stucture of finite dimensional algebras

Abstract

In this paper we study possible relations between
the solutions of Conjugate systems of quadratic equations. We
compared the number of solutions by using the structure theorem
for a finite dimensional commutative associative algebras with
identity. Also we have presented our investigations of the problem
into using the structure theorem for a finite dimensional Jordan
Algebra. Application in Biology is highlighted.
Index Terms—Conjugate System, quadratic equations, commutative
associative algebra, Jordan algebra