Results 51 to 60 of about 1,169,182 (223)
IDENTITIES WITH MULTIPLICATIVE GENERALIZED (α,α)-DERIVATIONS OF SEMIPRIME RINGS
Kragujevac Journal of MathematicsLet R be a semiprime ring and α be an automorphism of R. A mapping F : R → R (not necessarily additive) is called multiplicative generalized (α,α)-derivation if there exists a unique (α,α)-derivation d of R such that F(xy) = F(x)α(y) + α(x)d(y) for all x,
G. Sandhu, A. Ayran, Neşet Aydın
semanticscholar +1 more source
Notes on Semiprime Ideals with Symmetric Bi-Derivation
AxiomsIn this paper, we prove many algebraic identities that include symmetric bi-derivation in rings which contain a semiprime ideal. We intend to generalize previous results obtained for semiprime rings with symmetric derivation using semiprime ideals in ...
Ali Yahya Hummdi +3 more
doaj +1 more source
On multiplicative centrally-extended maps on semi-prime rings
Journal of Taibah University for Science, 2022 In this paper, we show that for semi-prime rings of two-torsion free and 6-centrally torsion free, given a multiplicative centrally-extended derivation δ and a multiplicative centrally-extended epimorphism ϕ we can find a central ideal K and maps ...
M. S. Tammam EL-Sayiad, A. Ageeb
doaj +1 more source
A note on a pair of derivations of semiprime rings
International Journal of Mathematics and Mathematical Sciences, 2004 We study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)∈Z(R) for all x∈R, then f and g are ...
Muhammad Anwar Chaudhry, A. B. Thaheem
doaj +1 more source
On Skew Left n-Derivations with Lie Ideal Structure
مجلة بغداد للعلوم, 2019 In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and the commutativity of Lie ideal under certain conditions were proved.
Faraj et al.
doaj +1 more source
On τ-centralizers of semiprime rings
Siberian Mathematical Journal, 2007 Summary: Let \(R\) be a semiprime 2-torsion free ring, and let \(\tau\) be an endomorphism of \(R\). Under some conditions we prove that a left Jordan \(\tau\)-centralizer of \(R\) is a left \(\tau\)-centralizer of \(R\). Under the same conditions we also prove that a Jordan \(\tau\)-centralizer of \(R\) is a \(\tau\)-centralizer of \(R\).
openaire +4 more sources
Prime Graphs of Polynomials and Power Series Over Noncommutative Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The prime graph PG(R) of a ring R is a graph whose vertex set consists of all elements of R. Two elements x, y ∈ R are adjacent in the graph if and only if xRy = 0 or yRx = 0. An element a ∈ R is called a strong zero divisor in R if 〈a〉〈b〉 = 0 or 〈b〉〈a〉 = 0 for some nonzero element b ∈ R. The set of all strong zero divisors is denoted by S(R).
Walaa Obaidallah Alqarafi +3 more
wiley +1 more source
Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this article, instead of a generalized derivation, we will use the concept of a generalized semiderivation ∇ that satisfies various identities involving a prime ideal ß of an optional ring Λ to describe the behavior of a quotient ring Λ/ß. We will use this concept to generalize some well‐known results that studied the behavior of a ring Λ via a ...
Kholood Alnefaie, Pramita Mishra
wiley +1 more source
Skew $N$-Derivations on Semiprime Rings [PDF]
, 2012 For a ring $R$ with an automorphism $\sigma$, an $n$-additive mapping $\Delta:R\times R\times... \times R \rightarrow R$ is called a skew $n$-derivation with respect to $\sigma$ if it is always a $\sigma$-derivation of $R$ for each argument.
Wei Zhang +5 more
core +1 more source
A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let A be an arbitrary ring, α an automorphism of A, I a nonzero ideal of A, and ϒ a prime ideal of A satisfying the condition ϒ⊊αI. This research investigates the interplay between two generalized (α, α)‐derivations, Ω and G (associated with (α, α)‐derivations f and h, respectively), and the resulting characteristics of the quotient ring A/ϒ.
Ali Yahya Hummdi +4 more
wiley +1 more source