矩阵环的欧拉恒等式与标准多项式恒等式

Szigeti-Tuza和Revesz使用Swan图论定理构造了n×n矩阵环Mn（C）的欧拉恒等式1].本文中证明这些恒等式可由标准多项式生成,即：若欧拉图Γp,q从某顶点t到u（t,u可为同一点）至少有n条边,则该欧拉图对应的欧拉多项式fΓp,q（X）可由标准多项式Sn（X）生成.该结果不仅推广了Chang2]和Giambruno-Sehal3]的结果,而且找到由欧拉恒等式生成的T-理想的一个有限生成集.

Eulerian identites and standard polynomial identities for matrix rings

Using Swan＇s graph theoretic theorem,Szigeti-Tuza and Revesz constructed Eulerian identities of the n×n matrix ring Mn（C）1].In this paper,we showed that those identities could be generated by standard polynomical identities,i.e.If the Eulerian graph Γp,q had at least n edges starting at some vertex t and ending at some vertex u（t=u was allowed）,then Eulerian polynomial fΓp,q（X） can be generated by Sn（X）.By this result,the generalization of the results of chang2] and Giambruno-Sehgal3] were obtained,and also a finite generating set of the T-ideal generated by the Eulerian identities was found.