The Minimal Degree Standard Identity on M_nE² and M_nE³

2019/01/21 by Balázs, Barbara Anna, Mészáros, Szabolcs
#05C25 #05C45 #15A75 (secondary) #16R20 (primary) #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1901.07085

Abstract

We prove an Amitsur--Levitzki-type theorem for Grassmann algebras, stating that the minimal degree of a standard identity that is a polynomial identity of the ring of n × n matrices over the m-generated Grassmann algebra is at least 2\lfloor(m)/(2)\rfloor+4n-4 for all n,m≥ 2 and this bound is sharp for m=2,3 and any n≥ 2. The arguments are purely combinatorial, based on computing sums of signs corresponding to Eulerian trails in directed graphs.

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