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Canadian Mathematical Bulletin, 1983
AbstractLet R be a prime ring and dā 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 dā 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 Prime and Semiprime Rings with Derivations
Algebra Colloquium, 2006Let R be a ring and S a nonempty subset of R. A mapping f: R ā R is called commuting on S if [f(x),x] = 0 for all x ā 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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Mathematics and Mathematics Education, 2002
Jae Keol Park, Gary F. Birkenmeier
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Jae Keol Park, Gary F. Birkenmeier
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