Results 31 to 40 of about 299 (69)
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.
BaniΔ Iztok
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Ο-derivations on generalized matrix algebras
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 Let π be a commutative ring with unity, π, π be π-algebras, π¨ be (π, π)-bimodule and π© be (π, π)-bimodule. The π-algebra π’ = π’(π, π¨, π©, π) is a generalized matrix algebra defined by the Morita context (π, π, π¨, π©, ΞΎπ¨π©, Ξ©π©π¨).
Jabeen Aisha +2 more
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Two-Local derivations on associative and Jordan matrix rings over commutative rings [PDF]
, 2017 In the present paper we prove that every 2-local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has an extension to a derivation on the matrix ring over this associative ring.
arxiv +1 more source
A Study of Generalized Differential Identities via Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let R be a ring and P be a prime ideal of R. The aim of this research paper is to delve into the relationship between the structural properties of the quotient ring R/P and the behavior of generalized derivations in a ring R endowed with an involution.
Ali Yahya Hummdi +4 more
wiley +1 more source
Nonlinear generalized Jordan (Ο, Ξ)-derivations on triangular algebras
Special Matrices, 2018 Let R be a commutative ring with identity element, A and B be unital algebras over R and let M be (A,B)-bimodule which is faithful as a left A-module and also faithful as a right B-module.
Alkenani Ahmad N. +2 more
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On Additivity and Multiplicativity of Centrally Extended (Ξ±, Ξ²)βHigher Derivations in Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.In this paper, the concept of centrally extended (Ξ±, Ξ²)βhigher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (Ξ±, Ξ²)βhigher derivation is an (Ξ±, Ξ²)βhigher derivation.
O. H. Ezzat, Attila Gil nyi
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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:TβTd:{\mathcal{T}}\to {\mathcal{T}} in the infinite upper triangular ...
Zhang Daochang +3 more
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On Jordan mappings of inverse semirings
Open Mathematics, 2017 In this paper, the notions of Jordan homomorphism and Jordan derivation of inverse semirings are introduced. A few results of Herstein and BreΕ‘ar on Jordan homomorphisms and Jordan derivations of rings are generalized in the setting of inverse semirings.
Shafiq Sara, Aslam Muhammad
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On Jordan triple (Ο,Ο)-higher derivation of triangular algebra
Special Matrices, 2018 Let R be a commutative ring with unity, A = Tri(A,M,B) be a triangular algebra consisting of unital algebras A,B and (A,B)-bimodule M which is faithful as a left A-module and also as a right B-module.
Ashraf Mohammad +2 more
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On Generalized Derivations and Commutativity of Associative Rings
Discussiones Mathematicae - General Algebra and Applications, 2020 Let π be a ring with center Z(π). A mapping f : π β π is said to be strong commutativity preserving (SCP) on π if [f (x), f (y)] = [x, y] and is said to be strong anti-commutativity preserving (SACP) on π if f (x) β¦ f (y) = x β¦ y for all x, y βπ.
Sandhu Gurninder S. +2 more
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