Wyniki wyszukiwania - BazTech

1

Approximation of additive functional equations in NA Lie C*-algebras

Wang Z., Saadati R.

Demonstratio Mathematica

|

2018

|

Vol. 51, nr 1

37--44

EN

In this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation [wzór], where m ≥ 2.

2

Derivable maps and generalized derivations on nest and standard algebras

Pan Z.

Demonstratio Mathematica

|

2016

|

Vol. 49, nr 3

331--344

EN

For an algebra A, an A-bimodule M, and m (…) M, define a relation on A by RA(m, 0) = {(a, b) (…) A x A : amb = 0}. We show that generalized derivations on unital standard algebras on Banach spaces can be characterized precisely as derivable maps on these relations. More precisely, if A is a unital standard algebra on a Banach space X then (…)L(A,B(X)) is a generalized derivation if and only if (..) is derivable on RA(M,0), for some M (…) B(X). We give an example to show this is not the case in general for nest algebras. On the other hand, for an idempotent P in a nest algebra A = algN on a Hilbert space H such that P is either left-faithful to N or right-faithful to N﬩, if δ (…)L(A, B)H)) is derivable on RA(P, 0) then δ is a generalized derivation.

3

On (m, n)-derivations of some algebras

Shen Q., Li J., Guo J.

Demonstratio Mathematica

|

2014

|

Vol. 47, nr 3

672--694

EN

Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A + nBδ(A) for all A, B (…) A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA (…) 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.

4

On Jordan triple α-* centralizers of semiprime rings

Ashraf M., Mozumder M.R., Khan A.

Demonstratio Mathematica

|

2014

|

Vol. 47, nr 1

130--136

EN

Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R → R is called a left (resp. right) Jordan α-* centralizer associated with a function α : R → R if T(x2) = T(x)α(x*) (resp. T(x2) = α(x*)T(x)) holds for all x (…) R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R → R is an additive mapping such that 2T(xyx) = T(x)α(y*x*) + α(x*y*)T(x) holds for all x; y (…) R, then T is a Jordan α-* centralizer of R.

5

On derivations of operator algebras with involution

Širovnik N., Vukman J.

Demonstratio Mathematica

|

2014

|

Vol. 47, nr 4

784--790

EN

The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) (…) L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A (…) A(X). In this case, D is of the form D(A) = [A,B] for all A (…) A(X) and some fixed B (…) L(X), which means that D is a derivation.

6

Identities with generalized derivations in semiprime rings

Dhara B., Ali S., Pattanayak A.

Demonstratio Mathematica

|

2013

|

Vol. 46, nr 3

453--460

EN

Let R be a semiprime ring. 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) holds, for all x,y  R. The objective of the present paper is to study the following situations: (1) (...), for all x, y in some appropriate subset of R.

7

Genotoxicity of cyclopentha[c]phenanthrene and its two derivatives based on an in vitro micronucleus test

Rudnicka K., Łuczyński M. K., Góra M.

Environmental Biotechnology

|

2012

|

Vol. 8, No. 2

63--66

EN

Environmental pollution causes a variety of health problems, including cancer. Many known pollutants have carcinogenic properties and polycyclic aromatic hydrocarbons (PAH) belong to this group. In this study, an in vitro culture of V79 cells of the Chinese hamster was subjected to three tested PAHs: 5-amino-2,3-dihydro-1H-cyclopenta-[c]phenanthrene (ACP[c]Ph), 5-amino-9-methoxy-2,3-dihydro-1H-cyclopenta[c]phenanthrene (AMCP[c]Ph) and cyclopenta[c]phenanthrene (CP[c]Ph). The in vitro micronucleus (MN) assay was applied in order to evaluate the genotoxic properties of the studied compounds. The highest genotoxic effect was observed for AMCP[c]Ph in a concentration of 0.02μg·ml-1. The genotoxic effect of the other two compounds was slightly lower.

8

Derivation with engel conditions on multilinear polynomials in prime rings

Dhara B.

Demonstratio Mathematica

|

2009

|

Vol. 42, nr 3

467-478

EN

Let R be a prime ring with extended centroid C and characteristic different from 2, d a nonzero derivation of R, f(x1,..., xn) a nonzero multilinear polynomial over C such that [d2(f(x1,... , xn)),d(f(x1,... ,xn))]k = 0 for all x1,... ,xn in some nonzero right ideal [...] of R, where k is a fixed positive integer. If d(p) p [..]0, then pC = eRC for some idempotent e in the socle of RC and /(x1,..., xn) is central-valued on eRCe.

9

Pairs of derivations on rings and Banach algebras

Wei F., Xiao Z.

Demonstratio Mathematica

|

2008

|

Vol. 41, nr 2

297-308

EN

We give a generalization of Vukman's theorem concerning a pair of derivations on rings. Then applying this purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.

10

On (m, n)-Jordan derivations and commutativity of prime rings

Vukman J.

Demonstratio Mathematica

|

2008

|

Vol. 41, nr 4

773-778

11

On left multipliers and the commutativity of prime rings

Ashraf M., Ali S.

Demonstratio Mathematica

|

2008

|

Vol. 41, nr 4

763-771

EN

Let R be an associative ring. An additive mapping H : R —> R is called a left multiplier if H(xy) = H(x)y, holds for all x, y e R. In this paper, we investigate commutativity of prime rings satisfying certain identities involving left multiplier. Some related results have also been discussed.

12

An identity with derivations on rings and Banach algebras

Fosner A., Fosner M., Vukman J.

Demonstratio Mathematica

|

2008

|

Vol. 41, nr 3

525-530

13

On some equations related to derivations in rings and Banach algebras

Vukman J., Kosi-Ulbl I.

Demonstratio Mathematica

|

2006

|

Vol. 39, nr 1

61-66

EN

The main purpose of this paper is to investigate additive mapping D : R -> R, where R is a (m + n +1)! and \m2 + n2 - m - n - 4mn\ -torsion free semiprime ring with the identity element, satisfying the relation 2D(xm+n+l) = (m+-n+1)(xmD(x)xn +-xnD(x)xm), for all is an element of R and some integers m > 1, n > 1, m2 + n2 - m - n - 4mn /=0.

14

On alfa-derivations of prime and semiprime rings

Vukman J.

Demonstratio Mathematica

|

2005

|

Vol. 38, nr 2

283--290

EN

In this paper we investigate identities with alfa-derivations on prime and semiprime rings. We prove, for example, the following result. If D : R - R is an alfa-derivation of a 2 and 3-torsion free semiprime ring R such that [D(x},x2] = 0 holds, for all x is an element of R, then D maps R into its center. The results of this paper are motivated by the work of Thaheem and Samman [20].

15

Generalized finite operators

Mecheri S.

Demonstratio Mathematica

|

2005

|

Vol. 38, nr 1

163--167

EN

Let B(H) be the algebra of all bounded linear operators on an infinite dimensional complex and separable Hilbert space H. A infinity B(H) is called finite if \\AX - XA - I\\ > 1, VX infinity B(H). In this paper we extend the class of finite operators to a more general class of pairs of operators called generalized finite operators defined by {(A, B) infinity B(H) x B(H) : \\AX - XB - I\\ > 1, VX infinity B(H)} and we present some pairs of generalized finite operators.

16

On (α, β)-derivations of semiprime rings, II

Chaudhry M., Thaheem A.

Demonstratio Mathematica

|

2004

|

Vol. 37, nr 4

793--802

17

On semiderivations of prime rings

Ashrat M., Rehman N.

Demonstratio Mathematica

|

2004

|

Vol. 37, nr 2

275--284

18

On Jordan ideals and Jordan derivations of prime rings

Ashrat M., Rehman N.

Demonstratio Mathematica

|

2004

|

Vol. 37, nr 3

517--523

EN

Let R be a 2-torsion free prime ring, and let J be a nonzero Jordan ideal and a subring of R. In the present paper it is shown that if d is an additive mapping of R into itself satisfying d(u2) = d(u)u + ud(u), for all u 6 J, then d(uv) = d(u)v + ud(v), for all u, v J.

19

Centralizing mappings and derivations on semiprime rings

Chaudhry M., Thaheem A.

Demonstratio Mathematica

|

2004

|

Vol. 37, nr 2

285--292

EN

In this paper we study some properties of centralizing mappings on semi-prime rings. The main purpose is to prove the result: Let -R be a semiprime ring and f an endomorphism of R, g an epimorphism of R such that the mapping x -> [f(x),g(x)] is central. Then [f(x),g(x)] = 0 holds for all x e R. We also establish some results about (alpha,beta)-derivations.