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arXiv · 2602.14195

Bicomplex Algebraic Numbers

Hichem Gargoubi·Sayed Kossentini
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Abstract

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.

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Hichem Gargoubi, Sayed Kossentini. 2026-02-15. Bicomplex Algebraic Numbers. https://arxiv.org/abs/2602.14195

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