Maja Fošner

On the Extended Centroid of Prime Associative Superalgebras with Applications to Superderivations

Abstract The extended centroid of prime associative superalgebras is studied. As applications we obtain the superalgebra versions of some known theorems on derivations and functional identities in associative prime rings.

On a class of projections on *-rings

ABSTRACT In this article we describe the structure of projections acting on semiprime *-rings and satisfying a certain functional identity. The main result is applied to bicircular projections on C *-algebras.

An equation related to two-sided centralizers in prime rings

In this paper we prove the following result: Let R be a prime ring and let T : R ? R be an additive mapping satisfying the relation nT(xn)=T(x)xn-1 + xT(x)xn-2 + ... + xn-1T(x) for all x in R where n > 1 is some fixed integer. If char(R) = 0 or n = char(R) ? 2, then T is of the form T(x) = ?x for all x in R and some fixed element ? in R where C is the extended centroid of R.

On Some Functional Equations in Rings

In this article we prove the following result. Let n ≥ 1 be some fixed integer, and let R be a prime ring with 2n ≤ char(R) ≠ 2. Suppose there exists an additive mapping T: R → R satisfying the relation for all x ∈ R. In this case, T is of the form 4T(x) = qx + xq for all x ∈ R, where q is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections.

Approximate Cubic Lie Derivations

We study the stability and hyperstability of cubic Lie derivations on normed algebras. At the end, we write some additional observations about our results.

On skew-commuting mappings in semiprime rings

Abstract In this paper we prove the following result. Let R be a n!-torsion free semiprime ring and let f :R → R be an additive mapping satisfying the relation f(x)xn + xnf(x) = 0 for all x ∈ R. In this case f = 0.

An identity in prime superalgebras

Abstract In this paper we investigate the functional identity in a prime associative superalgebras. We prove the following result. Suppose that there exists a nonzero additive mapping f = f0 + f1, on a prime associative superalgebra with char(R) ≠ 2, satisfying the relation [f (x), y2] = 0 for all x, y ∈ ℋ(). If is prime algebra then [f (), ] = 0 or [, ] = 0. 0 is prime algebra then [f (), ] = 0 and [, 0] = 0 or A is trivial. More- over, if C1 = 0 then f0(1) = 0 and f1(0) = 0.