Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$
In this paper we will characterize the structure of factor rings for $\mathbb{Z}\left[ \omega \right]$ where $\omega=\frac{-1+\sqrt{-3}}{2},$is a 3rd primitive root of unity. Consequently, we can recognize prime numbers(elements) and their ramifications in $\mathbb{Z}\left[ \omega \right]$.
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2013-07-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://test.armjmath.sci.am/index.php/ajm/article/view/90 |
| Summary: | In this paper we will characterize the structure of factor rings for $\mathbb{Z}\left[ \omega \right]$ where $\omega=\frac{-1+\sqrt{-3}}{2},$is a 3rd primitive root of unity. Consequently, we can recognize prime numbers(elements) and their ramifications in $\mathbb{Z}\left[ \omega \right]$.
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| ISSN: | 1829-1163 |