Results 31 to 40 of about 205 (70)
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
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
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
IMAGE ENCRYPTION USING THE INCIDENCE MATRIX
, 2018 The purpose of this article is to indicate the importance of using close planar rings in the construction of high efficiency balanced incomplete block (BIBD) plans, and how these can be used to encrypting the image.
A. Lakehal, A. Boua
semanticscholar +1 more source
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
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
Generalized (; )-derivations and Left Ideals in Prime and Semiprime Rings [PDF]
, 2017 Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! Rbe an (; )-derivation.
Ali, Asma, Rahaman, Hamidur
core +2 more sources
SOME RESULTS ON SEMIGROUP IDEALS IN PRIME RING WITH DERIVATIONS
, 2016 Let R be a prime ring, I be a nonzero semigroup ideal of R, d, g, h be derivations of R and a, b ∈ R. It is proved that if d(x) = ag(x)+h(x)b for all x ∈ I and a, b are not in Z(R) then there exists for some λ ∈ C such that h(x) = λ [a, x], g(x) = λ [b ...
A. Ayran
semanticscholar +1 more source
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
Direct sums of J‐rings and radical rings
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 3, Page 531-534, 1995., 1994 Let R be a ring, J(R) the Jacobson radical of R and P the set of potent elements of R. We prove that if R satisfies (∗) given x, y in R there exist integers m = m(x, y) > 1 and n = n(x, y) > 1 such that xmy = xyn and if each x ∈ R is the sum of a potent element and a nilpotent element, then N and P are ideals and R = N ⊕ P.
Xiuzhan Guo
wiley +1 more source