Cauchy-Riemann Equations for Treons

Alejandro Jesús Bermejo Valdés

doi:10.20944/preprints202407.0103.v1

Preprint Communication Version 1 This version is not peer-reviewed

Version 1 : Received: 29 June 2024 / Approved: 1 July 2024 / Online: 1 July 2024 (13:26:58 CEST)

We explored an extension of the Cauchy-Riemann equations to the algebra of treons, recently described by Alejandro Bermejo, whose elements are ordered 3-tuples. We leveraged the isomorphism between the algebra of treons and algebra B, and deduced the Cauchy-Riemann equations for the algebra of treons, establishing the necessary conditions for analyticity in this algebraic structure. This work significantly broadened our horizons in complex analysis and introduced new possibilities for applications across various fields of advanced mathematics.

Cauchy-Riemann equations; treonic number; treons; algebra B; Bermejo's algebra

Computer Science and Mathematics, Algebra and Number Theory

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Cauchy-Riemann Equations for Treons

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