Derivations and Prime Ideals

We prove (under suitable characteristic restrictions) that if we have two derivations on a ring such that the product maps the ring into a prime ideal, then one of the derivations maps the ring into the prime ideal. We also prove that, if the product of two derivations leaves a prime ideal invariant...

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Veröffentlicht in:	Mathematical proceedings of the Royal Irish Academy 1998-12, Vol.98A (2), p.223-225
1. Verfasser:	Creedon, T.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Integers Logical proofs Mathematical rings Mathematical theorems
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creator	Creedon, T.
description	We prove (under suitable characteristic restrictions) that if we have two derivations on a ring such that the product maps the ring into a prime ideal, then one of the derivations maps the ring into the prime ideal. We also prove that, if the product of two derivations leaves a prime ideal invariant, then one of the derivations must leave the prime ideal invariant, and that a derivation leaves a semiprime ideal invariant if and only if some iterate of the derivation leaves the semiprime ideal invariant.
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issn	1393-7197
language	eng
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source	Jstor Complete Legacy
subjects	Algebra Integers Logical proofs Mathematical rings Mathematical theorems
title	Derivations and Prime Ideals
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