Jordan Martix Algebras Defined By Generators And Relations

In the present paper we use generators and relations to define free factor algebra of Jordan matrix algebras.We can gain the minimum number of Jordan matrix algebras under certain assumptions.The main four results are as follows:1.we use generators and relations to define Jordan matrix algebras,then we prove that Jordan matrix algebra over any field can be generated by 3 elements;2.we prove that the minimum number of generators of Jordan matrix algebras over a special field is 2;3.we give an interesting result about generators of Jordan matrix algebras over arbitrary fields;4.we prove that the minimum number of generators of the Jordan matrix algebras of all symmetric matrices of a matrix algebra.