Phrase guide

Eisenstein integer

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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Pronunciation

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1

noun

Meaning 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].

Definition source: English Wiktionary via Wiktextract

Topics: algebra, mathematics, sciences

Examples

  • 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 simplify.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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