In commutative ring theory, a branch of mathematics, the radical of an ideal I is an ideal such that an element x is in the radical if some power of x is in I. A radical ideal (or semiprime ideal) is an ideal that is its own radical (this can be phrased as being a fixed point of an operation on ideals called 'radicalization'). The radical of a primary ideal is prime.
Radical ideals defined here are generalized to noncommutative rings in the Semiprime ring article.
Read more about Radical Of An Ideal: Definition, Examples, Properties, Applications
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