ideal number

名词 n.
中文释义

英文释义

名词 n.
  1. An algebraic integer that represents an ideal in the ring of integers of a number field.
    — 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 the Advancement of Science, page 133, 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 quotient ϕ₁(α)=F(α)÷ϕ(α) is always ideal; for if ϕ₁(α) were an actual number, ϕ(α), which is the quotient of F(α) divided by ϕ₁(α), ought also to be an actual number.

词形变化

ideal numbers plural

词源

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.
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