Results 31 to 40 of about 263 (93)
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
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
Semiderivations Satisfying Certain Algebraic Identities on Jordan Ideals
, 2013 In this paper, we investigate commutativity of rings with involution in which derivations satisfy certain algebraic identities on Jordan ideals. Moreover, we extend some results for derivations of prime rings to Jordan ideals.
Vincenzo de Filippis +2 more
semanticscholar +1 more source
On structure of certain periodic rings and near‐rings
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 10, Page 667-672, 2000., 2000 The aim of this work is to study a decomposition theorem for rings satisfying either of the properties xy = xpf(xyx)xq or xy = xpf(yxy)xq, where p = p(x, y), q = q(x, y) are nonnegative integers and f(t) ∈ tℤ[t] vary with the pair of elements x, y, and further investigate the commutativity of such rings.
Moharram A. Khan
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
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Commutativity results for semiprime rings with derivations
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 471-474, 1998., 1996 We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x), d(y)] = 0 for all x, y ∈ R, to the case of semiprime rings. An extension of this result is proved for a two‐sided ideal but is shown to be not true for a one‐sided ideal.
Mohammad Nagy Daif
wiley +1 more source
ON CERTAIN DIFFERENTIAL IDENTITIES IN PRIME RINGS WITH INVOLUTION
, 2015 In the present paper we investigate commutativity of -prime ring R, which satisfies certain differential identities on -ideals of R. Some results already known for prime rings on ideals have also been deduced.
M. Ashraf, M. Siddeeque
semanticscholar +1 more source
Commutativity of one sided s‐unital rings through a Streb′s result
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 267-270, 1997., 1995 The main theorem proved in the present paper states as follows “Let m, k, n and s be fixed non‐negative integers such that k and n are not simultaneously equal to 1 and R be a left (resp right) s‐unital ring satisfying [(xmyk)n−xsy,x]=0 (resp [(xmyk)n−yxs,x]=0) Then R is commutative.” Further commutativity of left s‐unital rings satisfying the ...
Murtaza A. Quadri +2 more
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
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International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 1, Page 87-92, 1996., 1995 Let R be a ring, and let N and C denote the set of nilpotents and the center of R, respectively. R is called generalized periodic if for every x ∈ R\(N ⋃ C), there exist distinct positive integers m, n of opposite parity such that xn − xm ∈ N ⋂ C. We prove that a generalized periodic ring always has the set N of nilpotents forming an ideal in R.
Howard E. Bell, Adil Yaqub
wiley +1 more source