Geodesic
Length of a direct sum of nonassociative algebras
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 73-86

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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. 
@article{ZNSL_2019_482_a4,
     author = {A. E. Guterman and D. K. Kudryavtsev and O. V. Markova},
     title = {Length of a direct sum of nonassociative algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {73--86},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a4/}
}
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A. E. Guterman; D. K. Kudryavtsev; O. V. Markova. Length of a direct sum of nonassociative algebras. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 73-86. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a4/