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An Exposition Of The Eisenstein Integers, Sarada Bandara
An Exposition Of The Eisenstein Integers, Sarada Bandara
Masters Theses
In this thesis, we will give a brief introduction to number theory and prime numbers. We also provide the necessary background to understand how the imaginary ring of quadratic integers behaves.
An example of said ring are complex numbers of the form ℤ[ω] = {a+bω ∣ a, b ∈ ℤ} where ω2 + ω + 1 = 0. These are known as the Eisenstein integers, which form a triangular lattice in the complex plane, in contrast with the Gaussian integers, ℤ[i] = {a + bi ∣ a, b ∈ …