Almost PI algebras are PI

2019/10/13 by Larsen, Michael, Shalev, Aner
#16R99 #17B01 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1910.05764

Abstract

We define the notion of an almost polynomial identity of an associative algebra R, and show that its existence implies the existence of an actual polynomial identity of R. A similar result is also obtained for Lie algebras and Jordan algebras. We also prove related quantitative results for simple and semisimple algebras.

Related

• Nearly associative and nearly Hom-associative algebras and bialgebras
• Almost Lie nilpotent varieties of associative algebras
• Prime affine algebras of GK dimension two which are almost PI algebras
• PI theory for Associative Pairs
• Affine semiprime algebras of GK dimension one are (still) pi