Supercentralizing Superderivations on Prime Superalgebras

Abstract

Let A = A 0 ⊕ A 1 be an associative superalgebra over a commutative associative ring F , and let Z s A be its supercenter. An F -mapping f of A into itself is called supercentralizing on a subset S of A if x f x s ∈ Z s A for all x ∈ S. In this article, we prove a version of Posner's theorem for supercentralizing superderivations on prime superalgebras.

The Product of Generalized Superderivations on a Prime Superalgebra

“…Recently there has been a considerable authors who are interested in superalgebras. They extended many results of rings to superalgebras (see [3], [5], [6], [7], [8], [11], [16], [17] and [19]).…”

“…A superalgebra A is called a prime superalgebra if and only if aAb = 0 implies a = 0 or b = 0, where at least one of the elements a and b is homogeneous. The knowledge of superalgebras refers to [3], [5], [6], [7], [8], [16], [17] and [19].…”

On Skew-Supercommuting Maps in Superalgebras

“…In recent years, some results on maps of associative rings have been extended to superalgebras by several authors (see, for example, [1,2,7,[9][10][11]17]). In the present paper, we shall give a version of Brešar's theorem mentioned above for superalgebras.…”