Radical of an ideal
Concept in algebra / From Wikipedia, the free encyclopedia
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For other radicals, see radical of a ring.
In ring theory, a branch of mathematics, the radical of an ideal of a commutative ring is another ideal defined by the property that an element
is in the radical if and only if some power of
is in
. Taking the radical of an ideal is called radicalization. A radical ideal (or semiprime ideal) is an ideal that is equal to its radical. The radical of a primary ideal is a prime ideal.
This concept is generalized to non-commutative rings in the semiprime ring article.