Results 1 to 10 of about 427 (170)
On Prime Rings with Derivations
AxiomsThis paper identifies all derivations associated with two well-known non-commutative prime rings and provides some remarks on one of these derivations, called the prime derivation.
Khalid H. Al-Shaalan
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Semigroup ideal in Prime Near-Rings with Derivations [PDF]
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 rigid derivations in rings [PDF]
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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Stiff derivations of commutative rings [PDF]
Colloquium Mathematicum, 1984 Let \(d\) be a stiff derivation of a commutative ring \(R\); and let \(S=R[t,d]\) be the Ore extension of \(R\) by an indeterminate \(t\), such that \(tr=rt+d(r)\) for all \(r\) in \(R\). For any differential ideal \(I\) of \(R\), \(d\) is said to be stiff in \(I\) if \(S\cdot I\) is the only ideal of \(S\) which lies over \(I\).
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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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Commutativity of some Prime Nearrings using Left-Sided outer (σ, τ)-n-Derivation
UMYU Scientifica Journal, 2023 In the field of mathematics, pure mathematics is very important as it gives rise to the basis for the formation of all applicable mathematical concepts in solving real-life problems. Algebra is such an integral part of pure mathematics.
Ali Khan Moharram, Shamsu Ibrahim
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Derivations of commutative noetherian rings
Mathematische Zeitschrift, 1969 Wolmer V Vasconcelos
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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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On the commutativity of quotient near-rings under specific identities [PDF]
Arab Journal of Mathematical SciencesPurposeThe purpose of this paper is to investigate the commutativity of quotient near-rings endowed with a left derivation and a multiplier satisfying specific differential algebraic identities, and to clarify the role of the 3-prime condition in this ...
Slimane El Amrani, Abderrahmane Raji
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On commutativity of rings with generalized derivations
Journal of the Egyptian Mathematical Society, 2016 Let \(R\) be a ring, and let \(m\) and \(n\) be fixed positive integers. For given \(x,y\in R\), define extended anti-commutators inductively by \(x\circ_1 y=x\circ y=xy+yx\) and \(x\circ_k y=(x\circ_{k-1}y)\circ y\) for \(k>1\). It is proved that if \(R\) is prime with nonzero ideal \(I\), and \(R\) admits a generalized derivation \(F\) with nonzero ...
Rehman, Nadeem ur +2 more
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