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AbstractIn this paper, we generalize the classical method used to classify nilpotent low-dimensional Lie algebras to serve for nilpotent Bol algebras. The algebraic classification of the nilpotent Bol algebras up to dimension four is given. [ABSTRACT FROM AUTHOR]

Let (T,⟨⋅,⋅,⋅⟩) be a triple system of arbitrary dimension, over an arbitrary base field 𝔽 and in which any identity on the triple product is not supposed. A basisofTis called multiplicative if for anyi,j,k ∈ I, we have thatfor somer ∈ I. We show that ifTadmits a multiplicative basis, then it decomposes as the orthogonal direct sumof well-described ideals admitting each one a multiplicative basis. Also, the minimality ofTis characterized in terms of the multiplicative basis and it is shown that, under a mild condition, the above direct sum is by the family of its minimal ideals. [ABSTRACT FROM PUBLISHER]