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  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  -Giambruno-Sehgal  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.
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