2023/01/13 by Danchev, Peter, Pojar, Andrada
#15A23 #15B33 #16S50 #16U60 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2301.05612
We explore the situation where all companion n × n matrices over a field F are weakly periodic of index of nilpotence 2 and prove that this can be happen uniquely when F is a countable field of positive characteristic, which is an algebraic extension of its minimal simple (finite) subfield, with all subfields of order greater than n. In particular, in the commuting case, we show even that F is a finite field of order greater than n. Our obtained results somewhat generalize those obtained by Breaz-Modoi in Lin. Algebra & Appl. (2016).