We introduce algebraic structures where a ternary symmetry replaces the usual positive-negative symmetry of R. From three copies of  we form a field  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  we obtain algebraic structures analogous to the finite-dimensional associative division algebras over R. Some applications in analysis, geometry and number theory are presented.

algebraic structures, number fields, algebraic extensions, Euler method of summation, entanglement.

Received: May 25, 2022; Accepted: June 22, 2022; Published: July 6, 2022

How to cite this article: Claude Gauthier, On tridemi-real number system and algebraic entanglement, JP Journal of Algebra, Number Theory and Applications 56 (2022), 71-94. http://dx.doi.org/10.17654/0972555522025

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