Topic: Eisenstein Integers and Their Algebraic Properties
Speaker: Abdul Hadi, S.Si., M.Sc.
Date: Friday, February 20, 2026
Time: 1:30 PM – 2:30pm
Location: Lecture Room 320, Masters/Doctoral Program in Mathematics, Building F, 3rd Floor
Moderator: Dy Outdom
Our PhD Abdul Hadi, S.Si., M.Sc., delivered a presentation entitled “Eisenstein Integers and Their Algebraic Properties” . In his talk, he introduced the Eisenstein integers as a number system obtained by adjoining a complex cube root of unity to the ordinary integers.
He continued by discussing the algebraic structure of the ring, including how addition and multiplication are defined. A significant part of the presentation focused on the unit elements. Unlike the integers, which have only two units, the Eisenstein integers have six units. He explained how this richer unit structure affects divisibility and factorization properties.
Hadi then introduced the norm function and described its important role in studying arithmetic properties. He explained that the norm is multiplicative and can be used to define associates and to distinguish between irreducible and composite elements. Using the norm, he presented the classification of prime elements in the Eisenstein integers, including primes that remain prime, primes that split, and those related to the rational prime three.