Noncentral Square Research Articles

Results on Lie ideals of prime rings with homoderivations

Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping H on R is called a homoderivation if H(xy) = H(x)H(y)+H (x) y+xH(y) for all x, y ∈ R. In this paper we investigate homoderivations satisfying certain differential identities on square closed Lie ideals of prime rings.

Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Abstract Let be the triangular algebra consisting of unital algebras A and B over a commutative ring R with identity 1 and M be a unital (A; B)-bimodule. An additive subgroup L of A is said to be a Lie ideal of A if [L;A] ⊆ L. A non-central square closed Lie ideal L of A is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on A, every generalized Jordan triple higher derivation of L into A is a generalized higher derivation of L into A.

On Generalized Jordan Triple (σ,τ)-Higher Derivations in Prime Rings

Let R be a ring and let U be a Lie ideal of R. Suppose that σ,τ are endomorphisms of R, and ℕ is the set of all nonnegative integers. A family F={fn}n∈ℕ of mappings fn:R→R is said to be a generalized (σ,τ)-higher derivation (resp., generalized Jordan triple (σ,τ)-higher derivation) of R if there exists a (σ,τ)-higher derivation D={dn}n∈ℕ of R such that f0=IR, the identity map on R, fn(a+b)=fn(a)+fn(b), and fn(ab)=∑i+j=nfi(σn-i(a))dj(τn-j(b)) (resp., fn(aba)=∑i+j+k=nfi(σn-i(a))dj(σkτi(b))dk(τn-k(a))) hold for all a,b∈R and for every n∈ℕ. If the above conditions hold for all a,b∈U, then F is said to be a generalized (σ,τ)-higher derivation (resp., generalized Jordan triple (σ,τ)-higher derivation) of U into R. In the present paper it is shown that if U is a noncentral square closed Lie ideal of a prime ring R of characteristic different from two, then every generalized Jordan triple (σ,τ)-higher derivation of U into R is a generalized (σ,τ)-higher derivation of U into R.

On the square root of the centre of the Hecke algebra of type A

AbstractIn this paper we investigate non-central elements of the Iwahori-Hecke algebra of the symmetric group whose squares are central. In particular, we describe a commutative subalgebra generated by certain non-central square roots of central elements, and the generic existence of a rank-three submodule of the Hecke algebra contained in the square root of the centre, but not in the centre. The generators for this commutative subalgebra include the longest word and elements related to trivial and sign characters of the Hecke algebra. We find elegant expressions for the squares of such generators in terms of both the minimal basis of the centre and the elementary symmetric functions of Murphy elements.