AM  Vol.3 No.7 , July 2012
An Application of Eulerian Graph to PI on Mn(C)
ABSTRACT
We obtain a new class of polynomial identities on the ring of n × n matrices over any commutative ring with 1 by using the Swan’s graph theoretic method [1] in the proof of Amitsur-Levitzki theorem. Let be an Eulerian graph with k vertices and d edges. Further let be an integer and assume that . We prore that is an PI on Mn(C). Standard and Chang [2] -Giambruno-Sehgal [3] polynomial identities are the spectial examples of our conclusions.

Cite this paper
S. You, H. Zhao, Y. Feng and M. Cao, "An Application of Eulerian Graph to PI on Mn(C)," Applied Mathematics, Vol. 3 No. 7, 2012, pp. 809-811. doi: 10.4236/am.2012.37121.
References
[1]   R G. Swan. “An Application of Graph Theory to Algebra”, Proc. Amer. Math. Soc. Vol.14,1963, pp.367-373. Correction, Proc. Amer. Soc. Vol.21,1969, pp.379-380.

[2]   Q. Chang. “Some Consequences of the Standard Polynomial”. Proc. Amer. Math. Soc. Vol.104,1988, pp.707-710.

[3]   A. Giambruno. S K. Sehgal. “On a Polynomial Idntity for n?n Matrices”. J.Algebra, Vol.126,1989, pp.451-453.

[4]   S.F.You, Y.M.Zheng and D.G.Hu.“Eulerian Graph and Polynomial Identities on Matrix Rings”. Advances in Math. Vol.32,2003, pp.425-428

[5]   S.F.You. “The Primitivity of Extended Centroid Extension on Prime GPI-rings”. Advances in Math. Vol.29,2000, pp.331-336.

[6]   S.F.You. “The Essential (one-sided) Ideal of Semiprime PI-Rings”. Acta. Math. Sinica. Vol.44,2001, pp.747-752.

[7]   S.F.You, M.Cao and Y.J.Feng, “Semiautomata and Near Rings”, Quantitative Logic and Soft Computing 5, World Scientific, 2012, pp.428-431.

 
 
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