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.

Highlights

  • T sgn π xπ 1 xπ 2 xπ d 0 is an PI on M n 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

  • Eulerian path of symmetric group acting on the set 1, d and eπ i eπ i 1 for i 1, d 1

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Summary

Introduction

T sgn π xπ 1 xπ 2 xπ d 0 is an PI on M n C. Let and be the functions from E to V defined by es , es i, j where es is an edge from vertex i to vertex j. Let be an Eulerian graph with d edges e1, e2 , , ed and distinguished points p and q.

Results
Conclusion

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