Results 11 to 20 of about 6,477 (139)
Two-Local derivations on associative and Jordan matrix rings over commutative rings
Linear Algebra and its Applications, 2017 In the present paper we prove that every 2-local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has an extension to a derivation on the matrix ring over this associative ring.
Arzikulov, Farhodjon, Ayupov, Shavkat
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On derivations and commutativity in prime near-rings
Journal of Taibah University for Science, 2014 AbstractIn the present paper it is shown that zero symmetric prime right near-rings satisfying certain identities are commutative rings.
Ashraf, Mohammed +2 more
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A NOTE ON COMMUTATIVITY OF PRIME NEAR RING WITH GENERALIZED β-DERIVATION [PDF]
Matrix Science Mathematic, 2021 In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a prime near ring. If there exist 𝑢1 , 𝑣1 𝜖 𝑀 and two sided generalized β-derivation G associated with the nonzero two sided β-derivation 𝑔 on M ...
Abdul Rauf Khan +2 more
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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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Generalized Derivations with Commutativity and Anti-commutativity Conditions [PDF]
, 2007 Let R be a prime ring with 1, with char(R) ≠ 2; and let F : R → R be a generalized derivation. We determine when one of the following holds for all x,y ∈ R: (i) [F(x); F(y)] = 0; (ii) F(x)ΟF(y) = 0; (iii) F(x) Ο F(y) = x Ο
Bell, Howard E., Rehman, Nadeem-ur
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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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Derivation Requirements on Prime Near-Rings for Commutative Rings
Jurnal Ilmu Dasar, 2019 Near-ring is an extension of ring without having to fulfill a commutative of the addition operations and left distributive of the addition and multiplication operations It has been found that some theorems related to a prime near-rings are commutative ...
Dian Winda Setyawati +2 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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An inner automorphism is only an inner automorphism, but an inner endomorphism can be something strange [PDF]
, 2011 The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given with ...
Bergman, George M.
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