In this paper, we study ad-nilpotent elements in Lie algebras arising from semiprime
associative rings R free of 2-torsion. With the idea of keeping under control the torsion of R …

Let $ R $ be a prime ring with center $ Z (R) $ and an automorphism $\alpha. $ A mapping
$\delta: R\to R $ is called multiplicative skew derivation if $\delta (xy)=\delta (x) y+\alpha …

This paper investigates the relationship between the commutativity of rings and the
properties of their multiplicative generalized derivations. Let F be a ring with a semiprime …

Let S be a semiprime ring. A function Θ: S→ S is defined as a multiplicative (generalized)-
derivation if there is a function η on S such that Θ (wu)= Θ (w) u+ w η (u) for every w, u∈ S …

In this study, the commutativity conditions with generalized derivations, which have not been
examined before, are discussed. Under these conditions, the subject of generalized …

Let R be a semiprime ring with center Z (R), λ be a nonzero left-sided ideal of R, 0≠ a∈ R
and F, G: R→ R be multiplicative (generalized)-derivations of R associated to the maps d, g …

In the present paper, we prove some commutativity theorems for a prime ring with involution
in which generalized derivations satisfy certain differential identities. Some well known …

This paper is focused on the commutativity of the laws of semiprime rings, which satisfy
some algebraic identities involving homoderivations on ideals. It provides new and notable …

Consider R to be an associative prime ring and K to be a nonzero dense ideal of R. A
mapping (need not be additive) F: R→ Qmr associated with derivation d: R→ R is called a …

Let R be a 2-torsion free semiprime ring with center Z (R) and λ a nonzero left sided ideal of
R. Let F, G: R→ R be multiplicative (generalized)-derivations associated with the map d: R→ …