Results 201 to 210 of about 327,963 (245)

Commutativity of rings with derivations

Acta Mathematica Hungarica, 2010
The authors extend a theorem of \textit{H. E. Bell} and \textit{M. N. Daif} [Acta Math. Hung. 66, No. 4, 337-343 (1995; Zbl 0822.16033)] proving that the commutativity of a unital prime ring with a non-zero derivation is equivalent to several conditions on derivations of some powers (Theorem 2.2). Under the additional assumption that the identity is in
Andima, S., Pajoohesh, H.
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Almost-Commutativity in Rings

Acta Mathematica Hungarica, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bell, H. E., Klein, A. A.
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A commutativity property for rings

Journal of Algebra and Its Applications, 2015
We provide a partial answer to the following question: Assume that R is a finite ring of order s such that for every two subsets M and N of cardinalities m and n respectively, there exist x ∈ M and y ∈ N such that xy = yx. What relations among s, m, n guarantee that R is commutative?
Bell, H. E., Zarrin, M.
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Non-commutative Henselian rings [PDF]

Journal of Algebra, 2009
Non-commutative Henselian rings are defined and some basic properties of them are discussed. It is shown that a local ring which is complete in the topology defined by its maximal ideal is Henselian provided that it is almost commutative.
Aryapoor, Masood,, Aryapoor, Masood, Masood Aryapoor   +2 more
exaly   +2 more sources

ON THE COMMUTING GRAPH OF RINGS

Journal of Algebra and Its Applications, 2011
Let R be a non-commutative ring. The commuting graph of R denoted by Γ(R), is a graph with vertex set R\Z(R) and two vertices a and b are adjacent if ab = ba. It has been shown that the diameter of Γ(R)c is less than 3. For a finite ring R we show that the diameter of Γ(R)c is one if and only if R is the non-commutative ring on 4 elements.
Omidi, G. R., Vatandoost, E.
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On semivalues on commutative rings

Periodica Mathematica Hungarica, 2016
The notion of a semivalue on an arbitrary unitary commutative ring is introduced, and two fundamental theorems concerning values on fields are extended to this general context.
Nilson C. Bernardes, Dinamérico P. Pombo   +1 more
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Metaideals in Commutative Rings

Algebra Colloquium, 2005
New examples of metaideals in commutative rings are constructed. It is proved that metaideals of a commutative ring form a sublattice of the lattice of all subrings, and for any subring A of a commutative ring P, there exists the largest subring Mid P (A) (called metaidealizer) in which A is a metaideal. Metaidealizers in several cases are described.
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On Commutative Splitting Rings

Proceedings of the London Mathematical Society, 1970
Abstract not ...
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Commutativity of Rings with Constraints on Commutators, II

Results in Mathematics, 2000
[For part I see ibid. 5, 123-131 (1985; Zbl 0606.16023).] The author proves commutativity of an associative ring \(R\) satisfying one of the following conditions: (1) for each \(x,y\in R\) there exists a co-monic polynomial \(p(t)\in tZ[t]\), such that \([x,y]=[x,y](p(xy)-p(yx))\); (2) for each \(x,y\in R\) there exist \(p(t),q(t)\in tZ[t]\) with \(q(t)
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On Commutativity of Rings With Derivations

Results in Mathematics, 2002
Let \(R\) be a ring, \(S\) a nonempty subset of \(R\), and \(Z\) the center of \(R\). For \(x,y\in R\) denote \(xy- yx\) by \([x, y]\) and \(xy + yx\) by \(x\circ y\). Let \(d\) be a derivation on \(R\). For prime \(R\) and \(S\) either an ideal or a Lie ideal, the authors study commutativity under the assumption that one of the following holds for all
Ashraf, Mohammad, Nadeem-ur-Rehman
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