Results 31 to 40 of about 166 (91)
A note on multiplicative (generalized)-derivations in prime rings
, 2016 Let R be a prime ring, 0 6= a ∈ R and I a nonzero ideal of R. A map F : R → R is called a multiplicative (generalized)-derivation if F (xy) = F (x)y + xg(y) fulfilled for all x, y ∈ R where g : R→ R is any map(not necessarily derivation).
H. Alhazmi
semanticscholar +1 more source
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
wiley +1 more source
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
wiley +1 more source
Derivations and Reverse Derivations in Semiprime Rings
, 2007 The notion of reverse derivation is studied and some properties are obtained. It is shown that in the class of semiprime rings, this notion coincides with the usual derivation when it maps a semiprime ring into its center.
M. Samman, S. Arabia, Nouf AlYamani
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On the Structure of Near‐Rings via P‐Semiderivations
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper introduces the concept of a P‐semiderivation on a near‐ring N, which serves as a generalization of the classical notion of a semiderivation. We investigate the fundamental properties of P‐semiderivations in relation to a nonempty subset P⊆N. The study primarily focuses on the structure of 3‐prime near‐rings that admit such mappings.
Ali Yahya Hummdi +4 more
wiley +1 more source
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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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this study, we investigate the behavior of semiprime ideals that satisfy certain algebraic identities using multiplicative (generalized) derivations. In addition, examples are provided to show that the limits imposed on the hypotheses of the different theorems are not superfluous.
Amal S. Alali +5 more
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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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Veterinary Dermatology, Volume 36, Issue 5, Page 668-678, October 2025.Background – Erythemato‐ceruminous otitis externa (ECOE) is commonly associated with Malassezia spp. and microbial imbalance. Hypothesis/Objective – To assess the clinical performance of an ear cleaner in dogs suffering from ECOE associated with Malassezia spp. overgrowth and to measure its impact on the microbiota. Conclusions and Clinical Relevance –
Amaury Briand +11 more
wiley +1 more source
IMAGE ENCRYPTION USING THE INCIDENCE MATRIX
, 2018 The purpose of this article is to indicate the importance of using close planar rings in the construction of high efficiency balanced incomplete block (BIBD) plans, and how these can be used to encrypting the image.
A. Lakehal, A. Boua
semanticscholar +1 more source