Muzibur Rahman Mozumder

On generalized (θ, φ)-derivations in semiprime rings with involution

The main purpose of this paper is to prove the following result: Let R be a 2-torsion free semiprime *-ring. Suppose that θ, φ are endomorphisms of R such that θ is onto. If there exists an additive mapping F: R → R associated with a (θ, φ)-derivation d of R such that F(xx*) = F(x)θ(x*) + φ(x)d(x*) holds for all x ∈ R, then F is a generalized (θ, φ)-derivation. Further, some more related results are obtained.

ON GENERALIZED (σ, τ)-BIDERIVATIONS IN RINGS

Let σ, τ be automorphisms of a ring R. In the present paper many concepts related to biadditive mappings of rings, viz. σ-left centralizer traces, symmetric generalized (σ, τ)-biderivations, σ-left bimultipliers and symmetric generalized Jordan (σ, τ)-biderivations are studied. Many results related to these concepts are given. It is established that every symmetric generalized (σ, τ)-biderivation of a prime ring of characteristic different from 2, can be reduced to a σ-left bimultiplier under certain algebraic conditions. Further, it is shown that every symmetric generalized Jordan (σ, τ)-biderivation of a prime ring of characteristic different from 2 is a symmetric generalized (σ, τ)-biderivation.

On Jordan Triple α-*Centralizers Of Semiprime Rings

Abstract Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R→R is called a left (resp. right) Jordan α-*centralizer associated with a function α: R→R if T(x2)=T(x)α(x*) (resp. T(x2)=α(x*)T(x)) holds for all x ∊ R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R→ R is an additive mapping such that 2T(xyx)=T(x) α(y*x*) +α(x*y*)T(x) holds for all x, y ∊ R, then T is a Jordan α-*centralizer of R