A map $ f $ on a ring $\cal A $ is said to be commuting if $ f (x) $ commutes with $ x $ for
every $ x\in\cal A $. The paper surveys the development of the theory of commuting maps …

Let ℛ be a prime ring of characteristic different from 2, 𝒰 its right Ututmi quotient ring, 𝒞 its
extended centroid, f (x 1,…, xn) a multilinear polynomial in n non-commuting variables over …

Commutativity preserving maps Page 1 Linear Algebra and its Applications 429 (2008) 1051–1070
Available online at www.sciencedirect.com www.elsevier.com/locate/laa Commutativity …

Let R be a ring, A= M n (R) and θ: A→ A a surjective additive map preserving zero Jordan
products, ie if x, y∈ A are such that xy+ yx= 0, then θ (x) θ (y)+ θ (y) θ (x)= 0. In this paper, we …

In this article, we prove the following result. Let n≥ 3 be some fixed integer and let R be a
prime ring with char (R)≠(n+ 1)! 2 n− 2. Suppose there exists an additive map** D: R→ R …

Characterizing left centralizers by their action on a polynomial Page 1 Publ. Math. Debrecen
64/3-4 (2004), 343–351 Characterizing left centralizers by their action on a polynomial By …

Let A= Mn (F) be the matrix algebra over a field F with an involution∗, where n⩾ 20.
Suppose that θ: A→ A is a bijective linear map such that θ (x) θ (y)= θ (y) θ (x)* for all x, y∈ A …

The main theorem states that all Lie and Jordan derivations from a von Neumann algebra-
bimodule are standard. Moreover, this statement is proved for some other classes of …

Lie gradings on associative algebras Page 1 Journal of Algebra 321 (2009) 264–283 Contents
lists available at ScienceDirect Journal of Algebra www.elsevier.com/locate/jalgebra Lie …

In the present survey the main results of the theory of functional identities are presented and
an analysis of the current state of this theory is given. Applications obtained in this direction …