Growth of Codimensions of Metabelian Algebras / M. V. Zaicev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 6. P. 15-20 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 233-237].
Numerical invariants of identities of nonassociative algebras are considered. It is proved that the codimension sequence of any finitely generated metabelian algebra has an exponentially bounded codimension growth. It is shown that the upper PI-exponent increases at most by 1 after adjoining an external unit. It is proved that for two-step left-nilpotent algebras the lower PI-exponent increases at least by 1.
Key words: identities, codimensions, metabelian algebras, PI-exponent.