Word.ws English Dictionary

Eisenstein integer

Eisenstein integer noun: a complex number of the form a+bω, where a and b are integers and ω is defined by the following two rules: (1) ω³=1 and (2) 1+ω+ω²=0; an element of the Euclidean domain ℤ[ω].

Noun

Eisenstein integer (plural Eisenstein integers)

  1. A complex number of the form a+bω, where a and b are integers and ω is defined by the following two rules: (1) ω³=1 and (2) 1+ω+ω²=0; an element of the Euclidean domain ℤ[ω].
    • To divide an Eisenstein integer a#43;b#92;omega by another Eisenstein integer c#43;d#92;omega, notice that (c#43;d#92;omega)(c#43;d)(c#43;d#92;omega²)#61;c³#43;d³; accordingly multiply both denominator and numerator (of the division expressed as a fraction) by (c#43;d)(c#43;d#92;omega²), then...

Forms of Eisenstein integer

pluralEisenstein integers

Origin of Eisenstein integer

Named after Gotthold Eisenstein (1823–1852), German mathematician.

Questions about Eisenstein integer

What does Eisenstein integer mean?
Eisenstein integer means a complex number of the form a+bω, where a and b are integers and ω is defined by the following two rules: (1) ω³=1 and (2) 1+ω+ω²=0; an element of the Euclidean domain ℤ[ω].
What part of speech is Eisenstein integer?
Eisenstein integer is a noun.
What is the plural of Eisenstein integer?
The plural of Eisenstein integer is Eisenstein integers.

Words near Eisenstein integer in the dictionary

  1. Eisenstadt
  2. Eisenstadtian
  3. Eisenstadts
  4. Eisenstaedt
  5. Eisenstein
  6. Eisenstein integer
  7. Eisenstein integers
  8. Eisenstein prime
  9. Eisenstein primes
  10. Eisensteinian
  11. Eisert

Source and license

Adapted from Wiktionary: Eisenstein integer (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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