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radical ideals

radical ideals is the plural of radical ideal.

Meaning of radical ideal

Noun

radical ideal (plural radical ideals)

  1. (commutative algebra, ring theory) An ideal I within a ring R that is its own radical (i.e., for any r ∈ R, if rⁿ ∈ I for some positive integer n, then r ∈ I).
    • Any intersection of radical ideals is again a radical ideal. Since not every intersection of prime ideals is a prime ideal, it follows that not all radical ideals are prime.1981, Harry C. Hutchins, Examples of Commutative Rings, Polygonal Publishing House, page 3
    Synonyms:
    semiprime ideal

Questions about radical ideals

What is radical ideals the plural of?
Radical ideals is the plural of radical ideal.

Words near radical ideals in the dictionary

  1. radical feminist
  2. radical feminists
  3. radical hysterectomies
  4. radical hysterectomy
  5. radical ideal
  6. radical ideals
  7. radical ion
  8. radical ions
  9. radical line
  10. radical lines
  11. radical mastectomies

Source and license

Adapted from Wiktionary: radical ideals (page history and authors); radical ideal (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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