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 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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