Factor Rings and their decompositions in the Eisenstein integers Ring Z [ ω ]

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Submitted: 2024-12-19; Published: 2024-12-19

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Abstract

In this paper we will characterize the structure of factor rings for Z[ω]Z[ω] where ω=−1+√−32,ω=−1+−32,is a 3rd primitive root of unity. Consequently, we can recognize prime numbers(elements) and their ramifications in Z[ω]Z[ω].