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ON TRIDEMI-REAL NUMBER SYSTEM AND ALGEBRAIC ENTANGLEMENT
Keywords:
algebraic structures, number fields, algebraic extensions, Euler method of summation, entanglementDOI:
https://doi.org/10.17654/0972555522025Abstract
We introduce algebraic structures where a ternary symmetry replaces the usual positive-negative symmetry of $\mathbf{R}$. From three copies of $\mathbf{R}_{+}^*$, we form a field $\mathcal{T}$, where the associativity of the addition is assisted, and which can be seen as a system of three-ordered and entangled real numbers. By means of the algebraic doubling of $\mathcal{T}$, we obtain algebraic structures analogous to the finite-dimensional associative division algebras over $\mathbf{R}$. Some applications in analysis, geometry and number theory are presented.
Received: May 25, 2022
Accepted: June 22, 2022
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