Word.ws English Dictionary

factor ideal

factor ideal noun: for given ring R, any ideal I such that Q = R / I, the set of cosets of elements of I in R, is a ring (the quotient ring of I in R).

Noun

factor ideal (plural factor ideals)

  1. (ring theory) For given ring R, any ideal I such that Q = R / I, the set of cosets of elements of I in R, is a ring (the quotient ring of I in R).
    • 1965 [Prentice-Hall], Seth Warner, Modern Algebra, 1990, Dover, page 651,
      Consequently, we may speak of the sequence of invariant factor ideals of a finitely generated unitary module over a principal ideal domain A.
    • 1985 [W. H. Freeman and Company], Nathan Jacobson, Basic Algebra I, 2nd Edition, Dover, 2009, page 193,
      We shall now call the sequence of order ideals, ann z₁, ann z₂, ..., whose uniqueness has just been proved, the invariant factor ideals of the module M.

Forms of factor ideal

pluralfactor ideals

Questions about factor ideal

What does factor ideal mean?
Factor ideal means for given ring R, any ideal I such that Q = R / I, the set of cosets of elements of I in R, is a ring (the quotient ring of I in R).
What part of speech is factor ideal?
Factor ideal is a noun.
What is the plural of factor ideal?
The plural of factor ideal is factor ideals.

Words near factor ideal in the dictionary

  1. factor
  2. factor analyses
  3. factor analysis
  4. factor graph
  5. factor graphs
  6. factor ideal
  7. factor ideals
  8. factor II
  9. factor in
  10. factor IX
  11. factor market

Source and license

Adapted from Wiktionary: factor 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.

Last updated:

Cite this entry: “factor ideal.” Word.ws, https://word.ws/factor_ideal. Based on Wiktionary, CC BY-SA 4.0.