An Application of Eulerian Graph to PI on <i>Mn</i>(<i>C</i>)

• 作者: Hongyan Zhao Ming Cao Songfa You Yijun Feng
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: EULERIAN Graph EULERIAN Path ADMISSIBLE POLYNOMIAL IDENTITY
• 年，卷（期）: 2012,（7）
• 页码范围: 809-811
• 页数: 3页
• 分类号: O1

摘要

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.