Doctoral Dissertations

Abstract

"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 be written A= a₁+ea₂ where e is a basis element and a₁,a₂ are elements of the Cayley-Dickson algebra of next lower dimension. Results include the facts that for each real Cayley-Dickson algebra aⁱaʲ = aⁱ⁺ʲ and (aⁱb)aʲ = aⁱ(baʲ) for all integers i,j and any a,b in the algebra. The major result concerns zero divisors...."--Abstract, page ii.

Advisor(s)

Penico, Anthony J., 1923-2011

Committee Member(s)

Sawtelle, Peter G.
Hicks, Troy L.
Van Matre, Gene, 1929-1996
Pursell, Lyle E.
Haddock, Glen
Parks, William F.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1972

Pagination

v, 83 pages

Note about bibliography

Includes bibliographical references (pages 71-73).

Rights

© 1972 Harmon Caril Brown, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Cayley algebras
Ordered algebraic structures
Divisor theory
Noncommutative algebras

Thesis Number

T 2756

Print OCLC #

6034219

Electronic OCLC #

884585220

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Mathematics Commons

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