TITLE:
An Application of Eulerian Graph to PI on Mn(C)
AUTHORS:
Songfa You, Hongyan Zhao, Yijun Feng, Ming Cao
KEYWORDS:
Eulerian Graph; Eulerian Path; Admissible; Polynomial Identity
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.7,
June
19,
2012
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.