Derivations and Prime Ideals

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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Zusammenfassung: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.
ISSN:1393-7197