### A note on a pair of derivations of semiprime rings.

Chaudhry, Muhammad Anwar, Thaheem, A.B. (2004)

International Journal of Mathematics and Mathematical Sciences

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Chaudhry, Muhammad Anwar, Thaheem, A.B. (2004)

International Journal of Mathematics and Mathematical Sciences

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Feng Wei, Zhankui Xiao (2009)

Rendiconti del Seminario Matematico della Università di Padova

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Gerard Murphy (1994)

Banach Center Publications

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We survey some old and new results in the theory of derivations on Banach algebras. Although our overview is broad ranging, our principal interest is in recent results concerning conditions on a derivation implying that its range is contained in the radical of the algebra.

Tsiu-Kwen Lee (2005)

Studia Mathematica

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We discuss range inclusion results for derivations on noncommutative Banach algebras from the point of view of ring theory.

Volker Runde (1993)

Studia Mathematica

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Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes...

Silvana Mauceri (1990)

Rendiconti del Seminario Matematico della Università di Padova

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Martin Mathieu (1994)

Banach Center Publications

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With this paper, we intend to provide an overview of some recent work on a problem on unbounded derivations of Banach algebras that still defies solution, the non-commutative Singer-Wermer conjecture. In particular, we discuss several global as well as local properties of derivations entailing quasinilpotency in the image.

Matthew J. Heath (2010)

Banach Center Publications

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We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally,...

Khan, M.A., Khan, M.S. (2006)

Mathematica Pannonica

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De Filippis, V. (2006)

International Journal of Mathematics and Mathematical Sciences

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Öznur Gölbaşi, Emine Koç (2010)

Rendiconti del Seminario Matematico della Università di Padova

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Kim, Hark-Mahn, Kang, Sheon-Young, Chang, Ick-Soon (2008)

Journal of Inequalities and Applications [electronic only]

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Neshtiman Nooraldeen Suliman (2015)

Discussiones Mathematicae - General Algebra and Applications

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In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is shown that M is commutative if for all a,b ∈ I (I is an ideal of M) satisfying d(a) ∈ Z(M), and d(a ∘ b) = 0.