The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...

In this study, we define the generalized symmetric bi-derivation and its trace on MV-algebras give examples. We investigate some properties of bi-derivation’s trace. introduce isotone bi-additive bi-derivation. show that if A is a linearly ordered MV-algebra, Γ related to D γ , then = 0 or γ1 1

Definition 1.2. The module of relative differential forms of B over A is a Bmodule ΩB/A, together with an A-derivation d : B → ΩB/A satisfying the following universal property: for any B-module M and for any A-derivation d : B → M , there exists a unique B-module homomorphism f : ΩB/A → M such that d ′ = f ◦d. If DerA(B,M) denotes the set of all A-derivations from B into M , then we have a natu...

Let m,n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : R −→ R be a skew derivation of R and E(x) = D(xm+n+r)−D(xm)xn+r − xmD(xn)xr − xm+nD(xr). We prove that if E(x) = 0 for all x ∈ L, then D is a usual derivation of R or R satisfies s4(x1, . . . , x4), the standard identity of degree 4.

In the present paper we introduced the notion of (θ ,φ)-derivations of a BCI-algebra X . Some interesting results on inside (or outside) (θ ,φ)-derivations in BCI-algebras are discussed. It is shown that for any commutative BCI-algebra X , every inside (θ ,φ)derivation of X is isotone. Furthermore it is also proved that for any outside (θ ,φ)-derivation d(θ ,φ) of a BCI-algebra X , d(θ ,φ)(x) =...

The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let A(X) ⊆ L(X) be a standard operator algebra, and let T : A(X) → L(X) be an additive mapping satisfying the relation T (A2n+1) = 2n+1 ∑ i=1 (−1)i+1Ai−1T (A)A2n+1−i, for all A ∈ A(X) and some fixed integer n ≥ 1. In this case T ...

Let m ≥ 0, n ≥ 0 be fixed integers with m + n 6= 0 and let R be a ring. It is our aim in this paper to investigate additive mapping T : R → R satisfying the relation (m + n)T (x2) = mT (x)x + nxT (x) for all x ∈ R. This research is a continuation of our earlier work ([11]). Throughout, R will represent an associative ring with center Z(R). Given an integer n ≥ 2, a ring R is said to be n−torsio...

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

Let M be a 2-torsion free prime Γ-ring and X a nonzero faithful and prime ΓM -module. Then the existence of a nonzero Jordan left derivation d : M → X satisfying some appropriate conditions implies M is commutative. M is also commutative in the case that d : M → M is a derivation along with some suitable assumptions. AMS (MOS) Subject Classification Codes: 03E72, 54A40, 54B15