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Canadian Mathematical Bulletin, 1983
AbstractLet R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.
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AbstractLet R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.
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On the Multiplication Ring of a Prime Ring
Communications in Algebra, 2006Given a positive integer n, we show there is a positive integer f(n) with the following property. Let R be a prime ring with extended centroid C, and let a 1,a 2,…,a n be C-independent elements of R. Then there is an element in the multiplication ring of R such that m ≤ f(n), p(a 1) = 0 and p(a 2),…,p(a n ) are C-independent. A similar approach is used
M. Brešar, W. S. Martindale
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On Compact Prime Rings and their Rings of Quotients
Canadian Mathematical Bulletin, 1968In [10], it is defined that a right (or left) ideal I of a ring R is very large if the cardinality of R/I is finite. It is also proven in [10, Theorem 3.4] that if R is a prime ring with 1 such that its characteristic is zero, then R is a right order in a simple ring with the minimum condition on one sided ideals if every large right ideal of R is very
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Skew Derivations of Prime Rings
Siberian Mathematical Journal, 2006Summary: Given a prime ring \(R\), a skew \(g\)-derivation for \(g\colon R\to R\) is an additive map \(f\colon R\to R\) such that \(f(xy)=f(x)g(y)+xf(y)=f(x)y+g(x)f(y)\) and \(f(g(x))=g(f(x))\) for all \(x,y\in R\). We generalize some properties of prime rings with derivations to the class of prime rings with skew derivations.
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JORDAN *-DERIVATIONS OF PRIME RINGS
Journal of Algebra and Its Applications, 2014Let R be a prime ring, which is not commutative, with involution * and with Qms(R) the maximal symmetric ring of quotients of R. An additive map δ : R → R is called a Jordan *-derivation if δ(x2) = δ(x)x* + xδ(x) for all x ∈ R. A Jordan *-derivation of R is called X-inner if it is of the form x ↦ xa - ax* for x ∈ R, where a ∈ Qms(R).
Lee, Tsiu-Kwen, Zhou, Yiqiang
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Semiderivations and Commutativity in Prime Rings
Canadian Mathematical Bulletin, 1988AbstractA semiderivation of a ring R is an additive mapping f:R → R together with a function g:R → R such that f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y) and f(g(x) ) = g(f(x)) for all x, y ∊ R. Motivating examples are derivations and mappings of the form x → x — g(x), g a ring endomorphism.
Bell, H. E., Martindale, W. S. III
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2000
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Prime Ideals in Ring Extensions
Journal of the London Mathematical Society, 1983It is proved that if B is a (left and right) Noetherian ring, A a Noetherian subring of B and P a prime ideal of B then there is a naturally arising finite set X of prime ideals of A, containing the primes minimal over \(A\cap P\) and there are positive integers z(Q) (\(Q\in X)\) such that \[ rank(B/P)=\sum_{Q\in X}z(Q)rank(A/Q) \] where ''rank'' means
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S-Prime Ideals of a Commutative Ring
Beitrage Zur Algebra Und Geometrie, 2020Achraf Malek, Ahmed Hamed
exaly