Results 21 to 30 of about 6,477 (139)
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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Characterizations of derivations [PDF]
, 2019 The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations. In Chapter 2 we
Gselmann, Eszter
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Semigroup ideal in Prime Near-Rings with Derivations
مجلة بغداد للعلوم, 2011 In this paper we generalize some of the results due to Bell and Mason on a near-ring N admitting a derivation D , and we will show that the body of evidence on prime near-rings with derivations have the behavior of the ring.
Baghdad Science Journal
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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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Karpatsʹkì Matematičnì Publìkacìï, 2014 We prove that in a ring $R$ with an identity there exists an element $a\in R$ and a nonzero derivation $d\in Der R$ such that $ad(a)\neq 0$. A ring $R$ is said to be a $d$-rigid ring for some derivation $d \in Der R$ if $d(a)=0$ or $ad(a)\neq 0$ for all
O.D. Artemovych, M.P. Lukashenko
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On Hasse--Schmidt derivations: the action of substitution maps [PDF]
, 2018 We study the action of substitution maps between power series rings as an additional algebraic structure on the groups of Hasse--Schmidt derivations. This structure appears as a counterpart of the module structure on classical derivations.Comment: 42 ...
D Hoffmann +4 more
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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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Identities with derivations and automorphisms on semiprime rings
International Journal of Mathematics and Mathematical Sciences, 2005 The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative ...
Joso Vukman
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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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