"ideal" nach Englisch mit Beispielen - Kollokationen-Wörterbuch Englisch
- Rings which contain only one maximal ideal are called local rings.
- Frequently, R is a local ring and m is then its unique maximal ideal.
- The filtration of a local ring by the powers of its maximal ideal.
- By the above, any maximal ideal is prime.
- In commutative rings, there is no difference, and one speaks simply of maximal ideals.
- A ring with a unique maximal left ideal is a local ring.
- Any quotient of a ring by a maximal ideal is a simple ring.
- Every prime ideal of R is an intersection of maximal ideals.
- Every radical ideal is an intersection of maximal ideals.
- For example, is a maximal ideal in , but is not a field.
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