Word.ws English Dictionary

minimal ideal

minimal ideal noun: a nonzero (two-sided) ideal that contains no other nonzero two-sided ideal.

Noun

minimal ideal (plural minimal ideals)

  1. (ring theory) A nonzero (two-sided) ideal that contains no other nonzero two-sided ideal.
    • Of particular interest are the primitive rings with minimal ideals, algebraic algebras and algebras with a polynomial identity.1956, Nathan Jacobson, Structure of Rings, American Mathematical Society, page vii
    • Theorem 12. A semisimple ring R has only a finite number of minimal ideals and is their direct sum. Moreover, each minimal ideal is a simple ring.1970, Mary W. Gray, A Radical Approach to Algebra, Addison-Wesley, page 33

Forms of minimal ideal

pluralminimal ideals

Questions about minimal ideal

What does minimal ideal mean?
Minimal ideal means a nonzero (two-sided) ideal that contains no other nonzero two-sided ideal.
What part of speech is minimal ideal?
Minimal ideal is a noun.
What is the plural of minimal ideal?
The plural of minimal ideal is minimal ideals.

Words near minimal ideal in the dictionary

  1. minimajor
  2. minimajors
  3. minimal
  4. minimal brain dysfunction
  5. minimal change disease
  6. minimal ideal
  7. minimal ideals
  8. minimal media
  9. minimal medium
  10. minimal pair
  11. minimal pairs

Source and license

Adapted from Wiktionary: minimal 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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