Results 101 to 110 of about 6,477 (139)

Some commutativity theorems for prime rings with derivations and differentially semiprime rings

Some commutativity theorems for prime rings with derivations and differentially semiprime rings
openaire  

Some of the next articles are maybe not open access.

Related searches:

Ideals and Higher Derivations in Commutative Rings

Canadian Journal of Mathematics, 1972
In this paper, we wish to generalize the following lemma first proven by O. Zariski [5, Lemma 4]. Let O be a complete local ring containing the rational numbers and let m denote the maximal ideal of O. Assume there exists a derivation δ of O such that δ(x) is a unit in O for some x in m.
Brown, William C., Kuan, Wei-Eihn
openaire   +2 more sources

Higher derivations and commutativity in lattice-ordered rings

Positivity, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andima, S., Pajoohesh, H.
openaire   +1 more source

\(\Phi\)-derivations and commutativity of rings and algebras

2022
Summary: The main purpose of this paper is to investigate the effect of \(\Phi \)-derivatives on the commutativity of rings and algebras. Let \(\mathfrak{R}\) be a 2-torsion free prime ring, \(d: \mathfrak{R} \rightarrow \mathfrak{R}\) be a \(\Phi\)-derivation such that \(\Phi\) is an epimorphism and \(d\Phi = \Phi d = d\). If \([\Phi (a), \Phi (x)]d(y)
openaire   +1 more source

On derivations and commutativity in prime rings

Acta Mathematica Hungarica, 1995
Let \(R\) be a prime ring, \(U\) be a right ideal of \(R\), and \(d\) be a nonzero derivation of \(R\). It is shown that each of the following three conditions (i) \([d(x),d(y)] = d([y,x])\) for all \(x,y\in R\), (ii) \([d(x),d(y)] = d([x,y])\) for all \(x,y\in R\), (iii) \(\text{char\,}R\neq 2\) and \(d([x,y]) = 0\) for all \(x,y\in R\), implies that ...
Bell, H. E., Daif, M. N.
openaire   +2 more sources

On derivations and commutativity in semiprime rings

Communications in Algebra, 1995
Let R be a ring, Z its center, U a nonzero left ideal, and D:R → R a derivation. We show that if R is semiprime with suitably-restricted additive torsion, then R must contain nonzero central ideals if one of the following holds: (i) [x, [x, D(x)]] ∊ Z for all x ∊ U; (ii) for a fixed positive integer n, [xn, D(x)] ∊ Z for all x ...
Qing Deng, Howard E. Bell
openaire   +1 more source

Product and commuting generalized derivations in prime rings

Rendiconti del Circolo Matematico di Palermo Series 2, 2022
Let \(R\) be a (semi) prime ring and \(F:R\longrightarrow R\) an additive map. Recall that it is said \textit{derivation} of \(R\) if \(F(xy)=F(x)y+xF(y)\), for all \(x,y\in R\). Moreover, it is said \textit{generalized derivation} of \(R\) if there exists a derivation \(d:R\longrightarrow R\) such that \(F(xy)=F(x)y+xd(y)\), for all \(x,y\in R\).
openaire   +1 more source

Higher Derivations and Tensor Products of Commutative Rings

Canadian Journal of Mathematics, 1978
The genesis of this paper is the following well known result in field theory: Let R denote a field of characteristic p ≠ 0, and let denote a subfield of R such that for some e sufficiently large. Then R is isomorphic to the tensor product (over
openaire   +1 more source

Commuting Derivations and Automorphisms of Certain Nilpotent Lie Algebras Over Commutative Rings

Communications in Algebra, 2015
Let L be a finite-dimensional complex simple Lie algebra, L ℤ be the ℤ-span of a Chevalley basis of L, and L R  = R ⊗ℤ L ℤ be a Chevalley algebra of type L over a commutative ring R. Let 𝒩(R) be the nilpotent subalgebra of L R spanned by the root vectors associated with positive roots.
Zhengxin Chen, Bing Wang
openaire   +1 more source

On derivations involving prime ideals and commutativity in rings

São Paulo Journal of Mathematical Sciences, 2020
An additive mapping \(d\) defined on a ring \(R\) is called a derivation if \(d(xy)=d(x)y+xd(y)\) for all \(x,y \in R\). The results of this paper are separated in two parts. The first part is related to derivations involving prime ideals and the second part explains some special derivations. In the first result of the first part, the authors give some
A. Mamouni, L. Oukhtite, M. Zerra
openaire   +1 more source