1. On some equations related to derivations in ringsJoso Vukman, Irena Kosi-Ulbl, 2005, original scientific article Abstract: Let ▫$m$▫ and ▫$n$▫ be positive integers with ▫$m+n?0$▫, and let ▫$R$▫ be an ▫$(m+n+2)!$▫-torsion free semiprime ring with identity element. suppose there exists an additive mapping ▫$D:R? R$▫, such that ▫$D (x m+n+1)=(m+n+1)xmD (x)xn$▫ is fulfilled for all ▫$x?R$▫, then ▫$D$▫ is a derivation which maps $▫R$▫ into its center.
Keywords: mathematics, algebra, associative rings and algebras, derivations, prime rings, semiprime rings
Published in DKUM: 14.06.2017; Views: 1247; Downloads: 363
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2. Identities with derivations and automorphisms on semiprime ringsJoso Vukman, 2005, original scientific article Abstract: The purpose of the paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some results related to Posner's theorem as well as to Mayne's theorem are proved.
Keywords: mathematics, algebra, associative rings and algebras, derivations, prime rings, semiprime rings, automorphisms
Published in DKUM: 14.06.2017; Views: 1115; Downloads: 394
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3. 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
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4. 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
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5. An identity with derivations on rings and Banach algebrasAjda Fošner, Maja Fošner, Joso Vukman, 2008, original scientific article Abstract: The main purpose of this paper is to study the following: Let m, n, and $k_{i}, i = 1, 2, ..., n$ be positive integers and let $R$ be a $2m(m+ k_{1} + k_{2} + ... + k_{n} -1)!$-torsion free semiprime ring. Suppose that there exist derivations $D_{i} : R \to R, i = 1, 2, ..., n + 1$ , such that $D_{1}(x^{m})x^{k_{1}+...+k_{n}}+x^{k_{1}} D_{2}(x^{m})x^{k_{2}+...+k_{n}}+...+x^{k_{1}+...+k_{n}}D_{n+1}(x^{m})=0$ holds for all $x \in R$. Then we prove that $D_{1}+D_{2}+...+D_{n+1}=0$ and that the derivation $k_{1}D_{2}+(k_{1}+k_{2})D_{3}+...+(k_{1}+k_{2}+...+k{n})D_{n+1}$ maps $R$ into its center. We also obtain a range inclusion result of continuous derivations on Banach algebras.
Keywords: mathematics, algebra, associative rings and algebras, prime rings, Banach algebras, identities, derivations
Published in DKUM: 31.03.2017; Views: 1388; Downloads: 457
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6. Wei, Feng: Generalized differential identities of (semi-) prime rings. (English). - [J] Acta Math. Sin., Engl. Ser. 21, No.4, 823-832 (2005). [ISSN 1439-8516; ISSN 1439-7617]Matej Brešar, 2006, review, book review, critique Keywords: matematika, asociativni kolobarji, diferencialne identitete, prakolobarji, polprakolobarji, mathematics, associative rings, differential identities, prime rings, semiprime rings
Published in DKUM: 10.07.2015; Views: 1157; Downloads: 28
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7. Chen, T.-S.: Supercentralizing superderivations on prime superalgebras. (English). - [J] Commun. Algebra 33, No.12, 4457-4466 (2005). [ISSN 0092-7872; ISSN 1532-4125]Matej Brešar, 2006, review, book review, critique Keywords: matematika, asociativni kolobarji, prasuperalgebre, superodvajanja, Posnerjev izrek, supercentri, mathematics, associative rings, prime superalgebras, supercentralizing superderivations, Posner theorem, supercenters
Published in DKUM: 10.07.2015; Views: 1074; Downloads: 24
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8. Chebotar, M.A.; Ke, Wen-Fong; Lee, Pjek-Hwee: Maps characterized by action on zero products. (English). - [J] Pac. J. Math. 216, No.2, 217-228 (2004). [ISSN 0030-8730]Matej Brešar, 2006, review, book review, critique Keywords: matematika, asociativni kolobarji, ničelni produkti, prakolobarji, idempotenti, odvajanja, aditivne preslikave, mathematics, associative rings, ring isomorphisms, prime rings, idempotents, zero products, additive maps, additive maps
Published in DKUM: 10.07.2015; Views: 1040; Downloads: 34
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9. Lee, Tsiu-Kwen: Generalized skew derivations characterized by acting on zero products. (English). - [J] Pac. J. Math. 216, No.2, 293-301 (2004). [ISSN 0030-8730]Matej Brešar, 2006, review, book review, critique Keywords: matematika, asociativni kolobarji, posplošena poševna odvajanja, prakolobarji, idempotenti, ničelni produkti, aditivne preslikave, avtomorfizmi, mathematics, associative rings, generalized skew derivations, prime rings, idempotents, zero products, additive maps, automorphisms
Published in DKUM: 10.07.2015; Views: 1092; Downloads: 21
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10. Li, Pengtong; Lu, Fangyan: Additivity of elementary maps on rings. (English). - [J] Commun. Algebra 32, No.10, 3725-3737 (2004). [ISSN 0092-7872; ISSN 1532-4125]Matej Brešar, 2005, review, book review, critique Keywords: matematika, asociativni kolobarji, elementarne preslikave, aditivne preslikave, prakolobarji, operatorske algebre, mathematics, associative rings, elementary mappings, additive mappings, prime rings, operator algebras
Published in DKUM: 10.07.2015; Views: 1216; Downloads: 26
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