Results 1 to 10 of about 97 (96)
Derivations and commutativity of \sigma-prime rings
International Journal of Contemporary Mathematical Sciences, 2006 Summary: Let \(R\) be a \(\sigma\)-prime ring with characteristic not two and \(d\) be a nonzero derivation of \(R\) commuting with \(\sigma\). The purpose of this paper is to give suitable conditions under which \(R\) must be commutative.
Oukhtite, L., Salhi, S.
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On generalized derivations and commutativity of associative rings
Discussiones Mathematicae - General Algebra and Applications, 2020 Let be a ring with center Z(). A mapping f : → is said to be strong commutativity preserving (SCP) on if [f (x), f (y)] = [x, y] and is said to be strong anti-commutativity preserving (SACP) on if f (x) ◦ f (y) = x ◦ y for all x, y ∈. In the present paper, we apply the standard theory of differential identities to characterize SCP and SACP ...
Sandhu Gurninder S. +2 more
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COMMUTING AND 2-COMMUTING DERIVATIONS OF SEMIPRIME RINGS
Journal of Kufa for Mathematics and Computer, 2012 The main purpose of this paper is to study and investigate some results concerninggeneralized derivation D on semiprime ring R, we obtain a derivation d is commuting and 2-commuting on R.
Mehsin Jabel Atteya +1 more
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On commutators and derivations in rings
Journal of Algebra, 2004 Let \(a\) be a fixed element of the ring \(R\); and for each \(x_0\in R\), define higher commutators \(x_1,x_2,\dots\) inductively by \(x_i=[a,x_{i-1}]\). The authors' main purpose is to study when products \(b_ic_j\) or integer multiples of such products lie in the ideal generated by some power of \(a\).
Brešar, Matej +2 more
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Hearts for commutative Noetherian rings: torsion pairs and derived equivalences
Documenta Mathematica, 2021 Over a commutative noetherian ring R , the prime spectrum controls, via the assignment of support, the structure of both \mathsf{Mod}(R) and
Sergio Pavon, Jorge Vitoria
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On derivations and commutativity in prime rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 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.
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Prime gamma rings with centralizing and commuting generalized derivations [PDF]
International Journal of Algebra, 2013 Let $M$ be a prime $ $-ring satisfying a certain assumption and $D$ a nonzero derivation on $M$. Let $f:M\rightarrow M$ be a generalized derivation such that $f$ is centralizing and commuting on a left ideal $J$ of $M$. Then we prove that $M$ is commutative.
Hoque, Md Fazlul, Paul, A C
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Commutativity of rings and near-rings with generalized derivations
Indian Journal of Pure and Applied Mathematics, 2013 Let \(N\) be a 3-prime near-ring, and let \(f\) and \(g\) be nonzero generalized derivations on \(N\). Let \(V\) be a nonzero semigroup ideal of \(N\) -- i.e. a subset such that \(VN\subseteq V\) and \(NV\subseteq V\); and let \(U\) be a nonempty subset of \(N\). The authors explore the commutativity results which follow from the following hypotheses: (
Kamal, Ahmed A. M. +1 more
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Derivation of Commutative Rings and the Leibniz Formula for Power of Derivation [PDF]
Formalized Mathematics, 2021 Summary In this article we formalize in Mizar [1], [2] a derivation of commutative rings, its definition and some properties. The details are to be referred to [5], [7]. A derivation of a ring, say D, is defined generally as a map from a commutative ring A to A-Module M with specific conditions. However we start with simpler case, namely
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Generalized Derivations and Generalization of Co-commuting Maps in Prime Rings [PDF]
Taiwanese Journal of Mathematics, 2021 In the paper under review the authors study a functional identity involving three non-zero generalized derivations on a prime ring. More precisely, let \(R\) be a prime ring of characteristic different from \(2\), \(U\) its Utumi quotient ring, \(C\) its extended centroid, \(f(x_1,\ldots,x_n)\) a multilinear polynomial over \(C\), which is not central ...
Dhara, Basudeb +3 more
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