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1
Remarks on *-(σ, τ)-Lie ideals of *-prime rings with derivation
EN
Let R be a *- prime ring with characteristic not 2, U a nonzero *- (σ, τ)-Lie ideal of R, d a nonzero derivation of R. Suppose σ, τ be two automorphisms of R such that σd = dσ, τd = dτ and * commutes with σ, τ, d. In the present paper it is shown that if d(U) ⊆ Z or d2 (U) ⊆ Z, then U ⊆ Z.
2
Derivable maps and generalized derivations on nest and standard algebras
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 basic properties of δ-prime and δ-semiprime rings
EN
We provide a self-contained discussion of the notions of δ-primeness and δ-semiprimeness for associative rings, possibly without identity. Some of the facts and properties presented in the article seem less known and quite difficult to find in standard reference sources.
PL
Praca jest "samowystarczalnym” omówieniem pojęć δ-pierwszości i δ-półpierwszości, rozważanych w algebrze nieprzemiennej. Wszystkie udowodnione w pracy twierdzenia stosują się i do pierścieni z jedynką, i do pierścieni bez jedynki. Część faktów i własności przedstawionych w pracy wydaje się mało znana i raczej trudna do odszukania w standardowej literaturze.
EN
The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. In this paper we investigate the lower bound of the higher-order nonlinearity of Niho Boolean functions f(x) = tr(λxd) over F2n, where... [formula]
5
On (m, n)-derivations of some algebras
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.
6
On Jordan triple α-* centralizers of semiprime rings
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.
7
On derivations of operator algebras with involution
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.
8
Identities with generalized derivations in semiprime rings
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.
9
A characterization of one-element p-bases of rings of constants
EN
Let Κ be a unique factorization domain of characteristic p > 0, and let ƒ ∈ Κ[χ1,..., χn] be a polynomial not lying in Κ[wzór]. We prove that Κ[wzór] is the ring of constants of a Κ-derivation of Κ[χ1,..., χn] if and only if all the partial derivatives of ƒ are relatively prime. The proof is based on a generalization of Freudenburg's lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.
10
Derivation with engel conditions on multilinear polynomials in prime rings
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.
11
Identities with two automorphisms on semiprime rings
EN
In this paper we investigate identities with two automorphisms on semiprime rings. We prove the following result: Let T, S : R approaches R be automorphisms where R is a 2-torsion free semiprime ring satisfying the relation T(x)x = xS(x) for all x is an element of R. In this case the mapping x approaches T(x) - x maps R into its center and T = S.
12
On some equations related to derivations in rings and Banach algebras
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.
13
Identities with products of (alpha, beta)-derivations on prime rings
EN
The main purpose of this paper is to prove the following result. Let R be a noncommutative prime ring of characteristic different from two and let D and G = 0 be (\alpha, beta)-derivations of R into itself such that G commutes with alpha and beta. If [D{x), G(x)] = 0 holds for all x is an eleemnt of R then D = lambdaG where lambda is an element from the extended centroid of R.
14
On alfa-derivations of prime and semiprime rings
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
Regular derivation and synonymy in an e-dictionary of Serbian
EN
In this paper we explore the relation between derivational morphology and synonymy in connection with an electronic dictionary, inspired by the work of Maurice Gross. The characteristics of this relation are illustrated by derivation in Serbian, which produces new lemmas with predictable meaning. We call this regular derivation. We then demonstrate how this kind of derivation is handled in text processing using a morphological e-dictionary of Serbian and a collection of transducers with lexical constraints. Finally, we analyze the cases of synonymy that include regular derivation in one aligned text.
16
On (α, β)-derivations of semiprime rings, II
17
On (alpha,beta)-derivations of semiprime rings
EN
We show that if alpha and beta are centralizing automorphisms and d a centralizing (alpha,beta)-derivation of a semiprime ring -R, then d is commuting. Some results on alpha-derivations and centralizing derivations of semiprime rings follow as applications of this result.
18
A note on (alpha)-derivations on semiprime rings
EN
In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.
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