Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

A celebrated result of Herstein [10, Theorem 6] states that a ring R must be commutative if[x,y]n(x,y)=[x,y] for all x, y ∈ R, wheren (x,y)>1 is an integer. In this paper, we investigate the structure prime satisfies identity F([x,y])n=F([x,y]) and σ([x,y])n=σ([x,y]), where F σ are generalized derivation automorphism respectively n>1a fixed

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

This study aims to develop and validate a new algorithm that incorporates distal colonoscopic findings to predict advanced proximal neoplasia (APN) in a Chinese asymptomatic population. We collected age, gender, and colonoscopic findings from a prospectively performed colonoscopy study between 2013 and 2015 in a large hospital-based endoscopy unit in Shanghai, China. Eligible subjects were allo...

recently, the algebraic theory of mv -algebras is intensively studied. in this paper, we extend the concept of derivation of $mv$-algebras and we give someillustrative examples. moreover, as a generalization of derivations of $mv$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $mv$-algebras.also, we investigate some properties of them.

An algebraic foundation for the derivation of geometric construction schemes transforming arbitrary polygons with n vertices into k-regular n-gons is given. It is based on circulant polygon transformations and the associated eigenpolygon decompositions leading to the definition of generalized Napoleon vertices. Geometric construction schemes are derived exemplarily for different choices of n an...

For the whole class of linear term rewriting systems and for each integer k, we define k-bounded rewriting as a restriction of the usual notion of rewriting. We show that the k-bounded uniform termination, the k-bounded termination, the inverse k-bounded uniform, and the inverse kbounded problems are decidable. The k-bounded class (BO(k)) is, by definition, the set of linear systems for which e...

i=o hold for each choice of / and g in A and k in { 1 , . . . , q}. A point derivation of infinite order is an infinite sequence {dk} of linear functional such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each fcSl, and degenerate if d1 = 0. Some of the terminology given in the previous paragraph was intr...