Results 11 to 20 of about 201 (72)
Generalized Derivations with Commutativity and Anti-commutativity Conditions [PDF]
, 2007 Let R be a prime ring with 1, with char(R) ≠ 2; and let F : R → R be a generalized derivation. We determine when one of the following holds for all x,y ∈ R: (i) [F(x); F(y)] = 0; (ii) F(x)ΟF(y) = 0; (iii) F(x) Ο F(y) = x Ο
Bell, Howard E., Rehman, Nadeem-ur
core +1 more source
On McCoy Condition and Semicommutative Rings [PDF]
, 2012 Let $R$ be a ring, $\sigma$ an endomorphism of $R$, $I$ a right ideal in $S=R[x;\sigma]$ and $M_R$ a right $R$-module. We give a generalization of McCoy's Theorem \cite{mccoy}, by showing that, if $r_S(I)$ is $\sigma$-stable or $\sigma$-compatible. Then $
Louzari, Mohamed
core +3 more sources
SOME RESULTS ON LIE IDEALS WITH SYMMETRIC REVERSE BI-DERIVATIONS IN SEMIPRIME RINGS I [PDF]
, 2021 Let R be a semiprime ring, U a square-closed Lie ideal of R and D : R R ! R a symmetric reverse bi-derivation and d be the trace of D: In the present paper, we shall prove that R commutative ring if any one of the following holds: i) d(U) = (0); ii)d(U ...
Gölbaşı, Öznur +1 more
core +1 more source
Lie nilpotency indices of symmetric elements under oriented involutions in group algebras [PDF]
, 2013 Let $G$ be a group and let $F$ be a field of characteristic different from 2. Denote by $(FG)^+$ the set of symmetric elements and by $\mathcal{U}^+(FG)$ the set of symmetric units, under an oriented classical involution of the group algebra $FG$.
Castillo, John H.
core +3 more sources
On Jordan ideals and left (θ, θ)‐derivations in prime rings
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 37, Page 1957-1964, 2004., 2004 Let R be a ring and S a nonempty subset of R. Suppose that θ and ϕ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ, ϕ)‐derivation (resp., Jordan left (θ, ϕ)‐derivation) on S if δ(xy) = θ(x)δ(y) + ϕ(y)δ(x) (resp., δ(x2) = θ(x)δ(x) + ϕ(x)δ(x)) holds for all x, y ∈ S.
S. M. A. Zaidi +2 more
wiley +1 more source
A Note on Multiplicative (Generalized) (α, β)-Derivations in Prime Rings
Annales Mathematicae Silesianae, 2019 Let R be a prime ring with center Z(R). A map G : R →R is called a multiplicative (generalized) (α, β)-derivation if G(xy)= G(x)α(y)+β(x)g(y) is fulfilled for all x; y ∈ R, where g : R → R is any map (not necessarily derivation) and α; β : R → R are ...
Rehman Nadeem ur +2 more
doaj +1 more source
Rings whose units commute with nilpotent elements
Mathematica, 2018 Rings with the property in the title are studied under the name of ”uni” rings. These are compared with other known classes of rings and since commutative rings and reduced rings trivially have this property, conditions which added to uni rings imply ...
G. Călugăreanu
semanticscholar +1 more source
A commutativity‐or‐finiteness condition for rings
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 54, Page 2863-2865, 2004., 2004 We show that a ring with only finitely many noncentral subrings must be either commutative or finite.
Abraham A. Klein, Howard E. Bell
wiley +1 more source
Some Results on (σ,τ)-Lie Ideals [PDF]
, 2007 In this note we give some basic results on one sided(σ,τ)-Lie ideals of prime rings with characteristic not 2.
Güven, Evrim +2 more
core +1 more source
Traces of permuting generalized $n$-derivations of rings
, 2018 Let n 1 be a fixed positive integer and R be a ring. A permuting n-additive map ̋ W Rn ! R is known to be permuting generalized n-derivation if there exists a permuting nderivation W Rn ! R such that ̋.x1;x2; ;xix 0 i ; ;xn/ D ̋.x1;x2; ;xi ; ;xn/x 0 i C
M. Ashraf, Almas Khan, M. R. Jamal
semanticscholar +1 more source