1. On certain functional equation in prime ringsMaja Fošner, Benjamin Marcen, Joso Vukman, 2022, original scientific article Abstract: The purpose of this paper is to prove the following result. Let R be prime ring of characteristic different from two and three, and let F:R→R be an additive mapping satisfying the relation F(x3)=F(x2)x−xF(x)x+xF(x2) for all x∈R. In this case, F is of the form 4F(x)=D(x)+qx+xq for all x∈R, where D:R→R is a derivation, and q is some fixed element from the symmetric Martindale ring of quotients of R.
Keywords: prime ring, derivation, Jordan derivation, functional equation, algebra
Published in DKUM: 12.06.2024; Views: 131; Downloads: 16
 Full text (2,25 MB)
This document has many files! More... |
2. Jordan maps and zero Lie product determined algebrasMatej Brešar, 2022, original scientific article Abstract: Let ▫$A$▫ be an algebra over a field ▫$F$▫ with ▫$\mathrm{char} (F) \ne 2$▫. If ▫$A$▫ is generated as an algebra by ▫$[[A,A],[A,A]]$▫, then for every skew-symmetric bilinear map ▫$\Phi:A \times A \to X$▫, where ▫$X$▫ is an arbitrary vector space over ▫$F$▫, the condition that ▫$\Phi(x^2,x)=0$▫ for all ▫$x \in A$▫ implies that ▫$\Phi(xy,z) +\Phi(zx,y) + \Phi(yz,x)=0$▫ for all ▫$x,y,z \in A$▫. This is applicable to the question of whether ▫$A$▫ is zero Lie product determined, and is also used in proving that a Jordan homomorphism from ▫$A$▫ onto a semiprime algebra ▫$B$▫ is the sum of a homomorphism and an antihomomorphism.
Keywords: bilinear map, zero Lie product determined algebra, derivation, Jordan derivation, Jordan homomorphism, functional identity
Published in DKUM: 18.08.2023; Views: 421; Downloads: 41
Full text (215,86 KB)
This document has many files! More... |
3. An Engel condition with an additive mapping in semiprime ringsMaja Fošner, Nadeem Ur Rehman, Joso Vukman, 2014, original scientific article Abstract: The main purpose of this paper is to prove the following result: Let n > 1 be a fixed integer, let R be a n!-torsion free semiprime ring, and let f : R -> R be an additive mapping satisfying the relation [f (x), x]n = [[. . . [[f (x), x], x], . . .], x] = 0 for all x = R. In this case [f (x), x] = 0 is fulfilled for all x = R. Since any semisimple Banach algebra (for example, C algebra) is semiprime, this purely algebraic result might be of some interest from functional analysis point of view.
Keywords: mathematics, algebra, semiprime rings, derivation
Published in DKUM: 27.06.2017; Views: 1266; Downloads: 548
Full text (104,05 KB)
This document has many files! More... |
4. On dependent elements in ringsJoso Vukman, Irena Kosi-Ulbl, 2004, original scientific article Abstract: Let R be an associative ring. An element ▫$a\in R$▫ is said to be dependent on a mapping ▫$F:R\to R$▫ in case ▫$F(x)a=ax$▫ holds for all ▫$x\in R$▫. In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated. We prove, for example, that in case we have a semiprime ring R, there are no nonzero elements which are dependent on the mapping ▫$\alpha + \beta$▫, where an ▫$\alpha$▫ and ▫$\beta$▫ are automorphisms of R
Keywords: mathematics, algebra, rings, algebras, derivation, Jordan derivation, left centralizer, right centralizer, additive mapping, dependent elements
Published in DKUM: 14.06.2017; Views: 1090; Downloads: 376
Full text (1,83 MB)
This document has many files! More... |
5. An application of the Sakai's theorem to the characterization of H*-algebrasBorut Zalar, 1995, original scientific article Abstract: The well-known Sakai's theorem, which states that every derivation acting on a von Neumann algebra is inner, is used to obtain a new elegant proof of the Saworotnow's characterization theorem for associative ▫$H^\ast$▫-algebras via two-sided ▫$H^\ast$▫-algebras. This proof completely avoids structure theory.
Keywords: mathematics, functional analysis, ▫$H^\ast$▫-algebra, involution, automorphism, derivation, centralizer, von Neumann algebra
Published in DKUM: 14.06.2017; Views: 903; Downloads: 165
Full text (2,06 MB)
This document has many files! More... |
6. Integrations on ringsIztok Banič, 2017, original scientific article Abstract: In calculus, an indefinite integral of a function f is a differentiable function F whose derivative is equal to f. The main goal of the paper is to generalize this notion of the indefinite integral from the ring of real functions to any ring. We also investigate basic properties of such generalized integrals and compare them to the well-known properties of indefinite integrals of real functions.
Keywords: ring, integration, Jordan integration, derivation, Jordan derivation
Published in DKUM: 10.05.2017; Views: 1151; Downloads: 205
Full text (234,00 KB)
This document has many files! More... |
7. On derivations of operator algebras with involutionNejc Širovnik, Joso Vukman, 2014, original scientific article Abstract: 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.
Keywords: mathematics, prime rings, semiprime rings, derivation, Jordan derivation, Banach space
Published in DKUM: 31.03.2017; Views: 1197; Downloads: 354
Full text (343,43 KB)
This document has many files! More... |
8. On [(m, n)]-Jordan derivations and commutativity of prime ringsJoso Vukman, 2008, original scientific article Abstract: The purpose of this paper is to prove the following result. Let ▫$ m\geq\ge 1$▫, ▫$n \geq\ge 1$▫ be some fixed integers with ▫$m \ne n$▫, and let R be a prime ring with ▫$char (R) \ne 2mn (m+n) l, \vert m-n l, \vert$▫. Suppose there exists a nonzero additive mapping ▫$D : R \to R$▫ satisfying the relation ▫$(m + n)D(x^2) = 2mD(x)x + 2nxD(x)$▫ for all ▫$x \in R ((m,n)-Jordan derivation)$▫. If either ▫$char(R) = 0$▫ or ▫$char(R) \geq 3$▫ then D is a derivation and R is commutative.
Keywords: prime rings, derivation, Jordan derivation, commutativity
Published in DKUM: 31.03.2017; Views: 1258; Downloads: 553
Full text (87,88 KB)
This document has many files! More... |
9. On functional equations related to derivations in semiprime rings and standard operator algebrasNejc Širovnik, 2012, original scientific article Abstract: In this paper functional equations related to derivations on semiprime rings and standard operator algebras are investigated. We prove, for example, the following result, which is related to a classical result of Chernoff. Let ▫$X$▫ be a real or complex Banach space, let ▫$L(X)$▫ be the algebra of all bounded linear operators of ▫$X$▫ into itself and let ▫$A(X) subset L(X)$▫ be a standard operator algebra. Suppose there exist linear mappings ▫$D,G colon A(X) to L(X)$▫ satisfying the relations ▫$D(A^3)=D(A^2)A + A^2G(A)$▫, ▫$G(A^3) = G(A^2)A + A^2D(A)$▫ for all ▫$A in A(X)$▫. In this case there exists ▫$B in L(X)$▫ such that ▫$D(A) = G(A) = [A,B]$▫ holds for all ▫$A in A(X)$▫.
Keywords: matematika, algebra, prakolobar, polprakolobar, Banachov prostor, standardna operatorska algebra, odvajanje, jordansko odvajanje, jordansko trojno odvajanje, mathematics, algebra, prime ring, semiprime ring, Banach space, standard operator algebra, derivation, Jordan derivation, Jordan triple derivation
Published in DKUM: 10.07.2015; Views: 1479; Downloads: 68
 Link to full text |
10. On some functional equations arising from (m, n)-Jordan derivations and commutativity of prime ringsMaja Fošner, Joso Vukman, 2012, original scientific article Abstract: The purpose of this paper is to prove the following result. Let ▫$m, n ge 1$▫ be some fixed integers with ▫$m ne n$▫, and let ▫$R$▫ be a prime ring with ▫$(m+n)^2 < text{char} (R)$▫. Suppose a nonzero additive mapping ▫$D : R to R$▫ exists satisfying the relation ▫$(m+n)^2 D(x^3) = m(3m+n) D(x)x^2 + 4mnxD(x)x + n(3n+m)x^2 D(x)$▫ for all ▫$x in R$▫. In this case ▫$D$▫ is a derivation and ▫$R$▫ is commutative.
Keywords: matematika, prakolobar, polprakolobar, odvajanje, jordansko odvajanje, levo odvajanje, mathematics, prime ring, semiprime ring, derivation, Jordan derivation, left dderivation, left Jordan derivation, (m, n)-Jordan drivation
Published in DKUM: 10.07.2015; Views: 1292; Downloads: 88
Link to full text |
