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Full-Text Articles in Physical Sciences and Mathematics
Structure Of Zero Divisors, And Other Algebraic Structures, In Higher Dimensional Real Cayley-Dickson Algebras, Harmon Caril Brown
Structure Of Zero Divisors, And Other Algebraic Structures, In Higher Dimensional Real Cayley-Dickson Algebras, Harmon Caril Brown
Doctoral Dissertations
"Real Cayley-Dickson algebras are a class of 2ⁿ-dimensional real algebras containing the real numbers, complex numbers, quaternions, and the octonions (Cayley numbers) as special cases. Each real Cayley-Dickson algebra of dimension greater than eight (a higher dimensional real Cayley-Dickson algebra) is a real normed algebra containing a multiplicative identity and an inverse for each nonzero element. In addition, each element a in the algebra has defined for it a conjugate element ā analogous to the conjugate in the complex numbers. These algebras are not alternative, but are flexible and satisfy the noncommutative Jordan identity. Each element in these algebras can …