Polynomial Identities of Euler's Graphs and Matrix Rings.

In this paper, using Swan's graph theoretic method on directed path approach to Amitsur-Levitzki theorem, we obtain a new class of polynomial identities on the ring of n x n matrices over any commutative ring with 1. Standard and Chang-Giambruno-Sehgal polynomial identities are the special examples of our conclusions. [ABSTRACT FROM AUTHOR]