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.

We obtain a new class of polynomial identities on the ring of n

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.

S. You, H. Zhao, Y. Feng and M. Cao, "An Application of Eulerian Graph to PI on

References

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