Results 21 to 30 of about 205 (70)
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
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 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
Weakly periodic and subweakly periodic rings
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 33, Page 2097-2107, 2003., 2003 Our objective is to study the structure of subweakly periodic rings with a particular emphasis on conditions which imply that such rings are commutative or have a nil commutator ideal. Related results are also established for weakly periodic (as well as periodic) rings.
Amber Rosin, Adil Yaqub
wiley +1 more source
On generalized derivations as homomorphisms and anti-homomorphisms [PDF]
, 2004 The concept of derivations as well as generalized derivations (i.e. Ia,b(x) = ax + xb, for all a,b R) have been generalized as an additive function F : R R satisfying F(xy) = F(x)y + xd(y) for all x,y R, where d is a nonzero derivation on R.
Nadeem-úr Rehman
core +2 more sources
Generalized derivations on ideals of prime rings
, 2013 Let R be a prime ring. By a generalized derivation we mean an additive mapping g W R! R such that g.xy/D g.x/yCxd.y/ for all x;y 2 R where d is a derivation of R.
E. Albaş
semanticscholar +1 more source
A combinatorial commutativity property for rings
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 9, Page 525-530, 2002., 2002 We study commutativity in rings R with the property that for a fixed positive integer n, xS = Sx for all x ∈ R and all n‐subsets S of R.
Howard E. Bell, Abraham A. Klein
wiley +1 more source
On Commutativity of Rings with Generalized Derivations [PDF]
, 2002 The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for all x, y ∈ R, where d is a derivation on R, such a function F is said to be a ...
Rehman, Nadeem ur
core +1 more source
Strong commutativity preserving maps on triangular rings
, 2012 Let U = Tri(A ,M ,B) be a triangular ring. It is shown, under some mild assumption, that every surjective strong commutativity preserving map Φ : U →U (i.e. [Φ(T ),Φ(S)]= [T,S] for all T,S ∈ U ) is of the form Φ(T ) = ZT + f (T ) , where Z is in Z (U ) ,
X. Qi, J. Hou
semanticscholar +1 more source
Generalized periodic and generalized Boolean rings
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 8, Page 457-465, 2001., 2001 We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a generalized periodic, or a generalized Boolean, ring.
Howard E. Bell, Adil Yaqub
wiley +1 more source