We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with respect to the derivation subalgebra over an algebraically closed field with characteristic 0. Such pairs are the fundamental ingredients for constructing genera...

Let A be an algebra, and let θ, φ be ring automorphisms of A. An additive mapping H : A → A is called a θ, φ -derivation if H xy H x θ y φ x H y for all x, y ∈ A. Moreover, an additive mapping F : A → A is said to be a generalized θ, φ -derivation if there exists a θ, φ derivation H : A → A such that F xy F x θ y φ x H y for all x, y ∈ A. In this paper, we investigate the superstability of gene...

In this paper, we introduce the notion of a generalized f -derivation in a BEalgebra, and obtain some properties in generalized f -derivations. Also, we characterized isotone generalized f -derivations and KerD. Mathematics Subject Classification: 06F35, 03G25, 08A30

The concepts of derivation and centroid for Lie–Yamaguti algebras are generalized in this paper. A quasi-derivation a LY-algebra can be embedded as larger LY-algebra. relationship between quasi-derivations robustness has been studied.

Manual derivation of the dynamic model of a modular robot is almost impossible because it may have very different geometries and DOFS through module reconfiguration. This paper presents an algorithm to automatically generate the closed-form equation of motion of a modular robot from a kinematic graph based representation of the assembly configuration. We consider modular robots with the more ge...

Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GASmodule and every generalized supplement submodule is a direct summand of M if and only if M satisfies (P ∗); (3)...

Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

In this paper, we examine some questions concerned with certain “skew” properties of the range of a Jordan *-derivation. In the first part we deal with the question, for example, when the range of a Jordan *-derivation is a complex subspace. The second part of this note treats a problem in relation to the range of a generalized Jordan *-derivation.