Invention of Hypercomplex Numbers with Dimension 2 n and Preservation of Field Properties

This paper presents a novel construction of a hypercomplex number system with dimension 2n . Unlike existing systems such as octonions (n = 3) or sedenions (n = 4) where associativity is lost and zero divisors appear,etc this proposed system aims to preserve the algebraic structure of a field for n ≥ 2. By implementing a specific set of multiplication rules for the basis elements, we demonstrate that the resulting system maintains associativity, commutativity under addition, and lacks zero divisors, thereby expanding the potential applications in theoretical physics, artificial intelligence, and cryptography,etc