Let R be a ring with center Z and I a nonzero ideal of R. An additive mapping F : R → R is called a generalized derivation of R if there exists a derivation d : R → R such that F xy F x y xd y for all x, y ∈ R. In the present paper, we prove that if F x, y ± x, y for all x, y ∈ I or F x ◦ y ± x ◦ y for all x, y ∈ I, then the semiprime ring R must contains a nonzero central ideal, provided d I /...

In this paper, properties of ideal I semiprime ring R with multiplicative generalized (α,β)- reverse derivation determined not necessarily additive map d is studied. We previous studies for different derivations to F. show that [β(p),d(p)]I=0 all p∈I or [d(p)],α(p)]I=0 under the given conditions. Also, we give relationship between and anti-automorphism α automorphism β R. Under conditions, exam...

It is a famous conjecture that every derivation on each Banach algebra leaves every primitive ideal of the algebra invariant. This conjecture is known to be true if, in addition, the derivation is assumed to be continuous. It is also known to be true if the algebra is commutative, in which case the derivation necessarily maps into the (Jacobson) radical. Because I. M. Singer and J. Wermer origi...

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

let  be a banach algebra and  a derivation. in this paper, it is proved, under certain conditions, that , where  is the jacobson radical of . moreover, we prove that if  is unital and  is a continuous derivation, then , where  denotes the set of all primitive ideals such that  is commutative,  denotes the set of all maximal (modular) ideals such that  is commutative, and  is the set of all non-...

This article first explains concepts in taxometrics, including the meaning of "taxon" in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regres...

The DC transfer functions for the buck, boost, and Cuk PWM DC-DC converters in continuous conductionmodearell, l / ( l D ) , and-D/( l -D) respectively, ,where D is the duty cycle. Therefore. it is reasonable to expect that the Cuk PWh4 DC-DC converter circuit [l] can be synthesized by cascading boost and buck converter circuits. The purpose of this paper is to present a systematic and rigorous...

F [D] of Weyl type was defined and studied, where A is a commutative associative algebra with an identity element over a field F of arbitrary characteristic, and F [D] is the polynomial algebra of a commutative derivation subalgebra D of A. The 2-cocycles of a class of A[D] were determined by Su. In the present paper, we determine the 2-cocycles of a class of Lie superalgebras of Weyl type over...

Given an associative algebra satisfying the left commutativity identity abc = bac (Perm-algebra) with a derivation d, new operation a°b=ad(b) is left-symmetric (pre-Lie). We derive necessary and sufficient conditions for to be embeddable into differential Perm-algebra.