The Length of a Direct Sum of Nonassociative Algebras

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 nonassoc...

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Veröffentlicht in:	Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-08, Vol.249 (2), p.158-166
Hauptverfasser:	Guterman, A. E., Kudryavtsev, D. K., Markova, O. V.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Electric generators Lower bounds Mathematics Mathematics and Statistics Sharpness Upper bounds
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Beschreibung
Zusammenfassung:	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.
ISSN:	1072-3374 1573-8795
DOI:	10.1007/s10958-020-04929-4