Bicomplex Algebraic Numbers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918339808329728 |
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| author | Gargoubi, Hichem Kossentini, Sayed |
| author_facet | Gargoubi, Hichem Kossentini, Sayed |
| contents | We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct classes of extensions depending on the nature of the generating element. We further establish a key decomposition property for bicomplex extensions, which serves as a foundation for studying their rings of integers. We also observe that prime elements in the ring of integers of a number field may become semiprime in the rings of integers of suitable bicomplex extensions. Finally, we present two explicit examples of finite bicomplex extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14195 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bicomplex Algebraic Numbers Gargoubi, Hichem Kossentini, Sayed Number Theory We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct classes of extensions depending on the nature of the generating element. We further establish a key decomposition property for bicomplex extensions, which serves as a foundation for studying their rings of integers. We also observe that prime elements in the ring of integers of a number field may become semiprime in the rings of integers of suitable bicomplex extensions. Finally, we present two explicit examples of finite bicomplex extensions. |
| title | Bicomplex Algebraic Numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.14195 |