We prove that any multi-variate Hasse-Schmidt derivation can be decomposed in terms of substitution maps and uni-variate derivations. As a consequence we the bracket two $m$-integrable derivations is also $m$-integrable, for $m$ positive integer or infinity.

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

We will extend in this paper some results about commutativity of Jordan ideals proved [2] and [6]. However, we consider left derivations instead derivations, which is enough to get good relation the structure near-rings. also show that conditions imposed cannot be removed.

Several authors 1–4 have studied derivations in rings and near rings. Jun and Xin 5 applied the notion of derivation in ring and near-ring theory to BCI-algebras, and as a result they introduced a new concept, called a regular derivation, in BCI-algebras. Zhan and Liu 6 studied f-derivations in BCI-algebras. Alshehri 7 applied the notion of derivations to incline algebras. Alshehri et al. 8 int...

In this paper we consider the derivations for even part of the finitedimensional Hamiltonian superalgebra H over a field of prime characteristic. We first introduce an ideal N of H 0 and show that the derivation space from H 0 into W 0 can be obtained by the derivation space from N into W 0 , the even part of the generalized Witt superalgebra W . For further application we also give the generat...

We study termination of logic programs with dynamic scheduling, as it can be realised using delay declarations. Following previous work, our minimum assumption is that derivations are input-consuming, a notion introduced to define dynamic scheduling in an abstract way. Since this minimum assumption is sometimes insufficient to ensure termination, we consider here various additional assumptions ...

In this paper, we considered the properties of f -derivations of BCCalgebras. Also, we characterized Kerd by f -derivations. Mathematics Subject Classification: 06F35, 03G25, 08A30.