The notion of symmetric left bi-derivation of a BCI-algebra X is introduced, and related properties are investigated. Some results on componentwise regular and d-regular symmetric left bi-derivations are obtained. Finally, characterizations of a p-semisimple BCI-algebra are explored, and it is proved that, in a p-semisimple BCI-algebra, F is a symmetric left bi-derivation if and only if it is a...

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 have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

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

Let K,S,D be a division ring an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Viète formula and decompositions of differential operators. W -polynomials show up naturally, their connections with P -independency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations ...

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.

we are reporting on a patient with a large linear syringocystadenoma papiliferum present at birth over the anterior surface of the left leg. histologic findings and the results of immitnohlstochcmicat staining with monoclonal antihotlies cea and ikh-4 suggest derivation from eccrinc glands.

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.