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AbstractIn this paper, all biderivations of solvable Lie algebras of maximal rank g=Q⊕N are characterized. Namely, we consider a solvable Lie algebra of the form g=Q⊕N , where Q is the maximal torus subalgebra of g, N is the nilradical of g and dimQ=dimN/N2 .In the case dimQ=N we characterize the form of skew-symmetric and symmetric biderivations of g . As applications, the forms of linear commuting (skew-commuting) maps and the commutative post-Lie algebra structures on g are given. [ABSTRACT FROM AUTHOR]

It is shown that a finite-dimensional formally real simple Jordan algebra is completely determined by the relation of Jordan-orthogonality. Communicated by Prof. Alberto Elduque [ABSTRACT FROM AUTHOR]

We cryptanalyze a recently proposed matrix-based MOR cryptosystem. The security of the system depends on the difficulty of solving the following discrete logarithm problem: given an inner automorphism φ ofSL(d, 𝔽q) and φa(each given in terms of their images on generators ofSL(d, 𝔽q)), finda. We show that this problem can be reduced to a small number of similar problems in quotients of polynomial rings and solved in subexponential-time. [ABSTRACT FROM AUTHOR]

Let M n (R) be the algebra of all n × n matrices over a unital commutative ring R with 6 invertible, and let X be an R-module. It is shown that if a symmetric bilinear map {·, ·}: M n (R) × M n (R) → X satisfies the condition that {u, u} = 0 whenever u 2 = 0, then there exists a linear map f: [sl n (R)]2 → X such that {x, y} = f(x ○ y), ∀ x, y ∈ sl n (R), where sl n (R) denotes the subset of M n (R) of all matrices of trace zero. [ABSTRACT FROM PUBLISHER]