Navigation 
 Home 
 Search 
 Site map 

 Contact Graeme 
 Home 
 Email 
 Twitter

 Skip Navigation LinksMath Help > Sets, Set theory, Number systems > Number systems > Eisenstein Integer

An Eisenstein integer is a complex number of the form a+bω, where ω is one of the roots of unity,

ω = (-1/2 + i sqrt(3)/2),

and a,b are integers.

Eisenstein integers are members of the imaginary quadratic field Q(sqrt(-3))

Eisenstein integers form a ring, denoted Z[ω]

Eisenstein integers can be uniquely factored in terms of other Eisenstein integers (known as Eisenstein primes) up to powers of its units and rearrangements.

The units of Z[ω] are ±1, ±ω, and ±ω².

 . . . . . .

Internet references

Wikipedia:  Eisenstein integer

Mathworld: Eisenstein Integer

Related pages in this website

Complex number

Quadratic field

Gaussian integer


The webmaster and author of this Math Help site is Graeme McRae.