Daniel Eremita

TL;DR: The problem of describing the form of a bilinear map B : A × A → A satisfying B ( x, x ) x = x B (x, x ) for all x ∈ A is considered in this paper, where commutativity preserving maps and Lie isomorphisms of certain triangular algebras are determined.

TL;DR: In this article, the authors introduced the notion of multiplicative Lie n-derivation of a ring, generalizing the concept of a Lie triple derivation, and considered the question of when all multiplicative lie n-divergences of a triangular ring T have the so-called standard form.

TL;DR: In this paper, the problem of describing the form of additive maps F 1, F 2, G 1, G 2 : R → R satisfying functional identity F 1 ( x ) y + F 2 ( y ) x + xG 2 (y ) + yG 1 (x ) = 0 for all x, y ∈ R is considered.

TL;DR: Using the maximal left ring of quotients, the authors generalized the result on functional identity in triangular rings to the case of functional identity on commuting additive maps and generalized inner biderivations of triangular rings.

TL;DR: In this article, it was shown that if R is a 2-torsion free semiprime ring, then there exists an additive mapping T : R → R such that T(xyx) = T(x)yx − xT(y)x + xyT(x), where x is a fixed element in the symmetric Martindale ring of quotients of R.