Results 21 to 30 of about 166 (91)
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
On generalized derivations and commutativity of prime rings with involution
, 2017 Let R be a ring with involution ′∗′. A map δ of the ring R into itself is called a derivation if δ(xy) = δ(x)y + xδ(y) for all x, y ∈ R. An additive map F : R → R is called a generalized derivation on R if F(xy) = F(x)y + xδ(y) for all x, y ∈ R ...
Shakir Ali, H. Alhazmi
semanticscholar +1 more source
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
Multiplicative generalized derivations on Lie ideals in semiprime rings II
, 2017 Let R be a semiprime ring and L is a Lie ideal of R such that L 6 Z.R/. A map F WR!R is called a multiplicative generalized derivation if there exists a map d WR!R such that F.xy/D F.x/yCxd.y/; for all x;y 2 R: In the present paper, we shall prove that d
E. Koç, Öznur Gölbaşi
semanticscholar +1 more source
On derivations and commutativity in prime rings
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 70, Page 3859-3865, 2004., 2004 Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x), x], [d(y), y]] = 0, for all x, y ∈ I. We prove that if [I, I]I ≠ 0, then d(I)I = 0.
Vincenzo De Filippis
wiley +1 more source
, 2015 Let R be a semiprime ring with center Z.R/. A mapping F W R ! R is called a generalized derivation if there exists a derivation d WR!R such that F.xy/D F.x/yCxd.y/ holds for all x;y 2 R.
B. Dhara, S. Kar, Krishna Gopal Pradahan
semanticscholar +1 more source
On zero subrings and periodic subrings
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 7, Page 413-417, 2001., 2001 We give new proofs of two theorems on rings in which every zero subring is finite; and we apply these theorems to obtain a necessary and sufficient condition for an infinite ring with periodic additive group to have an infinite periodic subring.
Howard E. Bell
wiley +1 more source
, 2016 Let R be a ring with identity element and M be a right R-module. We say that M is weakly endo-prime if annS(N) is a prime ideal in the ring S = End(MR), for any nonzero fully invariant submodule N of M . In this paper we study this notion and obtain some
R. Beyranvand, P. K. Beiranvand
semanticscholar +1 more source
On Lie ideals and symmetric generalized (α, β)-biderivation in prime ring
Miskolc Mathematical Notes, 2019 Let R be a prime ring with char.R/¤ 2. A biadditive symmetric map WR R!R is called symmetric . ̨;ˇ/-biderivation if, for any fixed y 2R, the map x 7! .x;y/ is a . ̨;ˇ/derivation. A symmetric biadditive map W R R! R is a symmetric generalized .
N. ur Rehman, Shuliang Huang
semanticscholar +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 1, Page 55-57, 2000., 2000 For prime rings R, we characterize the set U∩CR([U, U]), where U is a right ideal of R; and we apply our result to obtain a commutativity‐or‐finiteness theorem. We include extensions to semiprime rings.
Howard E. Bell
wiley +1 more source