All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

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On some classes of nilpotent Leibniz algebras.

The nilpotency properties of the Leibniz algebra M n ( ℂ ) D .

Solvable Leibniz algebras with NF n ⊕ [...] F m 1 F m 1 nilradical

The nilpotency properties of the Leibniz algebra $M_{n} {(ℂ)}_{D}$ .

Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{matrix} F_{m}^{1} \end{matrix}$ nilradical