| 词汇 | nilradical |
| 释义 | BETA Examples of nilradicalnilradical isn’t in the Cambridge Dictionary yet. You can help! For purposes of comparison, consider the nilradical of a commutative ring, which consists of all elements that are nilpotent. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In the case of commutative rings, there is always a maximal nil ideal: the nilradical of the ring. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The nilradical is equal to the intersection of all the ring's prime ideals. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. There are, however, analogues of the nilradical defined for noncommutative rings, that coincide with the nilradical when commutativity is assumed. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The former condition ensures that the nilradical of the ring is zero, so that the intersection of all the ring's minimal primes is zero. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The first example of a radical was the nilradical introduced in, based on a suggestion in. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This ideal is the nilradical of the ring. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The singular radical contains the prime radical (the nilradical in the case of commutative rings) but may properly contain it, even in the commutative case. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The set of all nilpotent elements itself need not be an ideal (or even a subgroup), so the upper nilradical can be much smaller than this set. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. |
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