Results 21 to 30 of about 124 (48)
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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