Results 71 to 80 of about 97 (96)

Derivations, products of derivations, and commutativity in near-rings

2019
For a zero-symmetric 3-prime near-ring N, we study three kinds of conditions: (a) conditions involving two derivations d(1), d(2) which imply that d(1) = 0 or d(2) = 0; (b) conditions involving derivations which force (N, +) to be abelian or N to be a commutative ring; (c) the condition that d(n)(S) is multiplicatively central for some derivation d and
Argac, N, Bell, HE
openaire   +2 more sources

Commutativity conditions on derivations and Lie ideals $��$-prime rings

2009
Let $R$ be a 2-torsion free $ $-prime ring, $U$ a nonzero square closed $ $-Lie ideal of $R$ and let $d$ be a derivation of $R$. In this paper it is shown that: 1) If $d$ is centralizing on $U$, then $d = 0$ or $U \subseteq Z(R)$. 2) If either $d([x, y]) = 0$ for all $x, y \in U$, or $[d(x), d(y)] = 0$ for all $x, y \in U$ and $d$ commutes with ...
Oukhtite, L., Salhi, S., Taoufiq, L.
openaire   +1 more source

Commutativity and prime ideals in rings with involutions via derivations

Summary: This research explores the interplay between algebraic identities involving derivations with involutions and the commutativity of prime quotient rings. We aim to generalize established results that characterize commutativity in these rings.
Al-Omary, Radwan M., Rehman, Nadeem ur, Nisar, Junaid, Alnoghashi, Hafedh   +3 more
openaire   +2 more sources

Gold-Catalyzed Synthesis of Small Rings

Chemical Reviews, 2021
Mauro Mato, Allegra Franchino, Antonio M Echavarren   +2 more
exaly  

Ruthenium-Catalyzed Cycloadditions to Form Five-, Six-, and Seven-Membered Rings

Chemical Reviews, 2021
Rosalie S Doerksen, Tomáš Hodík, William G Shuler   +2 more
exaly  

Some commutativity theorems for prime rings with derivations and differentially semiprime rings

2016
Let \(R\) be a ring, \(U\) be a non-zero ideal of \(R\) and \(d\) be a derivation of \(R\). The results in this paper are of the type where commutativity relations involving images of elements of \(U\) under \(d\) are shown to be sufficient for \(R\) to be commutative. For example, Theorem 3 states that if \(R\) has no non-zero nilpotent \(d\)-ideal, \(
Hirano, Yasuyuki, Tominaga, Hisao
openaire   +2 more sources

Olympic rings framework

Nature Reviews Materials, 2022
exaly  

Biosynthesis and Metabolism of Cyclopropane Rings in Natural Compounds

Chemical Reviews, 2003
Ludger A Wessjohann, Wolfgang Brandt, Thies Thiemann   +2 more
exaly  

π-Conjugated molecules with fused rings for organic field-effect transistors: design, synthesis and applications

Chemical Society Reviews, 2010
Weiping Wu
exaly  

On Commutators Involving Derivations and Automorphisms in Prime Rings

2022
Mohd Arif Raza, Mohammad Shadab Khan, Nadeem ur Rehman   +2 more
openaire   +1 more source