Word.ws English Dictionary

ideal number

ideal number noun: an algebraic integer that represents an ideal in the ring of integers of a number field.

Noun

ideal number (plural ideal numbers)

  1. An algebraic integer that represents an ideal in the ring of integers of a number field.
    • This symbolic representation of ideal numbers is very convenient, and tends to abbreviate many demonstrations.
      Every ideal number is a divisor of an actual number, and, indeed, of an infinite number of actual numbers. Also, if the ideal number ϕ(α) be a divisor of the actual number F(α), the...1861, H. J. Stephen Smith, Report on the Theory of Numbers—Part II, Report of the Thirtieth Meeting of the British Association for the Advancement of Science, June-July 1860, British Association for...
    • 1992 [World Scientific], C. Y. Hsiung, Elementary Theory of Numbers, 1995, Allied Publishers, page 214,
      One of the most important developments of algebraic number theory is the creation of ideal numbers. All ideal numbers can be classified into ideal number classes. Both the study of ideal numbers...

Forms of ideal number

pluralideal numbers

Origin of ideal number

Apparently a calque of German ideale Zahl, a concept in number theory developed by German mathematician Ernst Kummer (1810—1893) and later incorporated by Richard Dedekind into the ring theory concept of ideal.

Questions about ideal number

What does ideal number mean?
Ideal number means an algebraic integer that represents an ideal in the ring of integers of a number field.
What part of speech is ideal number?
Ideal number is a noun.
What is the plural of ideal number?
The plural of ideal number is ideal numbers.

Words near ideal number in the dictionary

  1. ideal gas
  2. ideal gas law
  3. ideal gases
  4. ideal mixture
  5. ideal mixtures
  6. ideal number
  7. ideal numbers
  8. ideal point
  9. ideal points
  10. ideal polyhedra
  11. ideal polyhedron

Source and license

Adapted from Wiktionary: ideal number (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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