An Application of Eulerian Graph to PI on Mn(C)


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.

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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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The authors declare no conflicts of interest.


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