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://armjmath.sci.am/index.php/ajm/article/view/90 |
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doaj-a16ad9acc5e1477aab25d83eff253d772020-11-24T23:42:23ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632013-07-0151Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$Manouchehr Misaghian0Department of Mathematics, Prairie View A&M University Prairie View, TX 77446-USA 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 $\mathbb{Z}\left[ \omega \right]$. http://armjmath.sci.am/index.php/ajm/article/view/90 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Manouchehr Misaghian |
| spellingShingle |
Manouchehr Misaghian Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$ Armenian Journal of Mathematics |
| author_facet |
Manouchehr Misaghian |
| author_sort |
Manouchehr Misaghian |
| title |
Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$ |
| title_short |
Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$ |
| title_full |
Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$ |
| title_fullStr |
Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$ |
| title_full_unstemmed |
Factor Rings and their decompositions in the Eisenstein integers Ring ${\huge\mathbb{Z}}\left[ \omega \right]$ |
| title_sort |
factor rings and their decompositions in the eisenstein integers ring ${\huge\mathbb{z}}\left[ \omega \right]$ |
| publisher |
Republic of Armenia National Academy of Sciences |
| series |
Armenian Journal of Mathematics |
| issn |
1829-1163 |
| publishDate |
2013-07-01 |
| description |
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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| url |
http://armjmath.sci.am/index.php/ajm/article/view/90 |
| work_keys_str_mv |
AT manouchehrmisaghian factorringsandtheirdecompositionsintheeisensteinintegersringhugemathbbzleftomegaright |
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1725504702579212288 |