Results 301 to 310 of about 115,699 (314)

On the Multiplication Ring of a Prime Ring

Communications in Algebra, 2006
Given 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
W. S. Martindale rd, Matej Brešar
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Fully prime rings

Communications in Algebra, 1994
The structure of rings all of whose ideals are prime is studied and several examples of such rings are constructed.
William D. Blair, Hisaya Tsutsui
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Prime and Primitive Rings

1991
In commutative ring theory, three basic classes of rings are: reduced rings, integral domains, and fields. The defining conditions for these classes do not really make any use of commutativity, so by using exactly the same conditions on rings in general, we can define (and we have defined) the notions of reduced rings, domains, and division rings ...
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Derivations in Prime Rings

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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