矩阵环的欧拉恒等式与标准多项式恒等式  

Eulerian identites and standard polynomial identities for matrix rings

作　　者：冯怡君[1] 曹明[1] 魏亚萍[1] 游松发[1] 

机构地区：[1]湖北大学数学与计算机科学学院,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2013年第3期270-273,共4页Journal of Hubei University：Natural Science

摘　　要：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Chang[2]和Giambruno-Sehal[3]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.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 chang[2] and Giambruno-Sehgal[3] were obtained,and also a finite generating set of the T-ideal generated by the Eulerian identities was found.

关 键 词：欧拉图 欧拉路 欧拉恒等式 标准多项式恒等式 T-理想 

分 类 号：O153.3[理学—数学]