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Prime ideals and radicals in rings graded by clifford semigroups
Communications in Algebra, 1997exaly
ON GENERALIZED DERIVATIONS OF PRIME AND SEMIPRIME RINGS
Taiwanese Journal of Mathematics, 2012exaly
A theorem for prime rings [PDF]
Proceedings of the American Mathematical Society, 1979 Let n be a positive integer and let R be a prime ring either of characteristic zero or of characteristic
Anthony Richoux
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Generalized Derivations of Prime Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 LetRbe an associative prime ring,Ua Lie ideal such thatu2∈Ufor allu∈U. An additive functionF:R→Ris called a generalized derivation if there exists a derivationd:R→Rsuch thatF(xy)=F(x)y+xd(y)holds for allx,y∈R. In this paper, we prove thatd=0orU⊆Z(R)if any one of the following conditions holds: (1)d(x)∘F(y)=0, (2)[d(x),F(y)=0], (3) eitherd(x)∘F(y)=x ...
Huang Shuliang
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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. Also, it presents two results for some classes of non-commutative prime rings, regarding when the images of derivations on these rings are subrings of them.
Khalid H. Al-Shaalan
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On generalized homoderivations of prime rings
Matematychni Studii, 2023 Let $\mathscr{A}$ be a ring with its center $\mathscr{Z}(\mathscr{A}).$ An additive mapping $\xi\colon \mathscr{A}\to \mathscr{A}$ is called a homoderivation on $\mathscr{A}$ if $\forall\ a,b\in \mathscr{A}\colon\quad \xi(ab)=\xi(a)\xi(b)+\xi(a)b+a\xi(b).$ An additive map $\psi\colon \mathscr{A}\to \mathscr{A}$ is called a generalized ...
Rehman, N. +2 more
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Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 We first study connections between α-compatible ideals of R and related ideals of the skew Laurent polynomials ring R[x,x−1;α], where α is an automorphism of R.
Ebrahim Hashemı
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Commutativity Results on Prime Rings With Generalized Derivations [PDF]
Engineering and Technology Journal, 2016 Let R be a prime ring. For nonzero generalized derivations F and G associated with the same derivation d, we prove that if d≠0, then R is commutative, if any one of the following conditions hold: (1) [F(x), G(y)] 0, (2) F(x)oG(y) 0, (3) F(x)oG(y ...
A. Majeed, a Yass Shaima
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Quotient rings satisfying some identities
Cubo, 2023 This paper investigates the commutativity of the quotient ring \(\mathcal{R}/P\), where \(\mathcal{R}\) is an associative ring with a prime ideal \(P\), and the possibility of forms of derivations satisfying certain algebraic identities on \(\mathcal{R}\)
Mohammadi El Hamdaoui, Abdelkarim Boua
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