Results 21 to 30 of about 83 (83)
On Jordan ideals and left (θ, θ)‐derivations in prime rings
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 37, Page 1957-1964, 2004., 2004 Let R be a ring and S a nonempty subset of R. Suppose that θ and ϕ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ, ϕ)‐derivation (resp., Jordan left (θ, ϕ)‐derivation) on S if δ(xy) = θ(x)δ(y) + ϕ(y)δ(x) (resp., δ(x2) = θ(x)δ(x) + ϕ(x)δ(x)) holds for all x, y ∈ S.
S. M. A. Zaidi +2 more
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On derivations and commutativity in prime rings
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 70, Page 3859-3865, 2004., 2004 Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x), x], [d(y), y]] = 0, for all x, y ∈ I. We prove that if [I, I]I ≠ 0, then d(I)I = 0.
Vincenzo De Filippis
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σ-derivations on generalized matrix algebras
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 Let be a commutative ring with unity, 𝒜, be -algebras, be (𝒜, )-bimodule and 𝒩 be (, 𝒜)-bimodule. The -algebra 𝒢 = 𝒢(𝒜, , 𝒩, ) is a generalized matrix algebra defined by the Morita context (𝒜, , , 𝒩, ξ𝒩, Ω𝒩).
Jabeen Aisha +2 more
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Derivations of higher order in semiprime rings
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 89-92, 1998., 1997 Let R be a 2‐torsion free semiprime ring with derivation d. Supposed d2n is a derivation of R, where n is a positive integer. It is shown that if R is (4n − 2)‐torsion free or if R is an inner derivation of R, then d2n−1 = 0.
Jiang Luh, Youpei Ye
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Open Mathematics, 2017 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.
Banič Iztok
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Commutativity results for semiprime rings with derivations
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 471-474, 1998., 1996 We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x), d(y)] = 0 for all x, y ∈ R, to the case of semiprime rings. An extension of this result is proved for a two‐sided ideal but is shown to be not true for a one‐sided ideal.
Mohammad Nagy Daif
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International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 263-266, 1997., 1995 Let R be a ring A bi‐additive symmetric mapping d : R × R → R is called a symmetric bi‐derivation if, for any fixed y ∈ R, the mapping x → D(x, y) is a derivation. The purpose of this paper is to prove the following conjecture of Vukman. Let R be a noncommutative prime ring with suitable characteristic restrictions, and let D : R × R → R and f : x → D ...
Qing Deng
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A note on semiprime rings with derivation
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 413-415, 1997., 1996 Let R be a 2‐torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D : R → R a derivation. If d[x, y] + [x, y] ∈ Z or d[x, y] − [x, y] ∈ Z for all x, y ∈ I, then R is commutative.
Motoshi Hongan
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Additivity and Central Behavior of CE‐Generalized Homoderivations in Associative Rings
Journal of Mathematics, Volume 2026, Issue 1, 2026.This study examines the commutativity of a ring R endowed with a special class of mappings termed centrally extended generalized homoderivations. These mappings serve as an extension of several existing concepts, including homoderivations, generalized homoderivations, and left centralizers.
Hicham Saber +6 more
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Jordan left derivations in infinite matrix rings
Demonstratio MathematicaLet RR be a unital associative ring. Our motivation is to prove that left derivations in column finite matrix rings over RR are equal to zero and demonstrate that a left derivation d:T→Td:{\mathcal{T}}\to {\mathcal{T}} in the infinite upper triangular ...
Zhang Daochang +3 more
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