Results 281 to 290 of about 42,209 (310)

On Compact Prime Rings and their Rings of Quotients

Canadian Mathematical Bulletin, 1968
In [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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On Prime and Semiprime Rings with Derivations

Algebra Colloquium, 2006
Let R be a ring and S a nonempty subset of R. A mapping f: R → R is called commuting on S if [f(x),x] = 0 for all x ∈ S. In this paper, firstly, we generalize the well-known result of Posner related to commuting derivations on prime rings. Secondly, we show that if R is a semiprime ring and I is a nonzero ideal of R, then a derivation d of R is ...
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Skew Derivations of Prime Rings

Siberian Mathematical Journal, 2006
Summary: 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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Semiderivations and Commutativity in Prime Rings

Canadian Mathematical Bulletin, 1988
AbstractA 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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Prime and homogeneous rings and algebras

Algebra i logika, 2019
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, 1983
It 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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Derivations in prime rings.

2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Structure of a quotient ring $$\pmb {R/P}$$ with generalized derivations acting on the prime ideal P and some applications

Indian Journal of Pure and Applied Mathematics, 2021
Lahcen Oukhtite
exaly  

Prime ideals of the Burnside ring of a saturated fusion system

Journal of Algebra, 2022
Nicolas Lemoine
exaly  

2-PRIME IDEALS AND 2-PRIME RINGS

JP Journal of Algebra, Number Theory and Applications, 2021
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