A. E. Guterman, D. K. Kudryavtsev, O. V. Markova, “Length of a direct sum of nonassociative algebras”, Zap. Nauchn. Sem. POMI, 2019, Volume 482,Pages <nobr>73

Length of a direct sum of nonassociative algebras

A. E. Guterman^ab, D. K. Kudryavtsev^a, O. V. Markova^ab

^a Lomonosov Moscow State University
^b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region

Abstract: A lower and an upper bounds for the length of a direct sum of nonassociative algebras are obtained, and their sharpness is established. Note that while the lower bound for the length of a direct sum in the associative and nonassociative cases turns out to be the same, the upper bound in the nonassociative case significantly exceeds its associative counterpart.

Key words and phrases: non-associative algebra, length of an algebra, direct sum.

UDC: 512.554.1

Received: 08.10.2019