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Semiprime rings with prime ideals invariant under derivations. (English) Zbl 1109.16031

For semiprime rings \(R\), the following is an open question: Does there exist a family of prime ideals \(P_\alpha\), \(\alpha\in\Gamma\), such that \(\bigcap P_\alpha=\{0\}\) and each \(P_\alpha\) is invariant under all derivations of \(R\)? This paper provides an affirmative answer for countable rings and PI-rings. Of course, such an affirmative answer allows certain results on derivations in prime rings to be extended to semiprime rings, and the authors give an example extending a recent commutativity theorem of T.-K. Lee and C.-Y. Pan [Publ. Math. 61, No. 1-2, 75-85 (2002; Zbl 1006.16046)].

MSC:

16W25 Derivations, actions of Lie algebras
16N60 Prime and semiprime associative rings

Citations:

Zbl 1006.16046
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References:

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