The nonexistence of a factorization formula for Cayley numbers
Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 131-132
Voir la notice de l'article provenant de la source Cambridge University Press
Let C be the Cayley algebra denned over the real field. If, for given elements α, β, and γ of a quaternion subalgebra of C, α = βγ, it follows, by associativity, that for any nonzero element δ of the same quaternion subalgebra, α = (βδ)(δ-1γ). For Cayley numbers ζ ξ, and η with ζ = ξη, the relation ζ = (ξδ)(δ-1η) in general only holds when δ is a nonzero real number. Because of the existence of factorization results [1, 2] in the orders of C, the question naturally arises of whether it is possible to choose one-to-one mappings, θ and φ, of C onto itself such that ζ = θξ. φη whenever ζ = ξη. To discuss this question, we make the following definition.
Lamont, P. J. C. The nonexistence of a factorization formula for Cayley numbers. Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 131-132. doi: 10.1017/S001708950000519X
@article{10_1017_S001708950000519X,
author = {Lamont, P. J. C.},
title = {The nonexistence of a factorization formula for {Cayley} numbers},
journal = {Glasgow mathematical journal},
pages = {131--132},
year = {1983},
volume = {24},
number = {2},
doi = {10.1017/S001708950000519X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000519X/}
}
TY - JOUR AU - Lamont, P. J. C. TI - The nonexistence of a factorization formula for Cayley numbers JO - Glasgow mathematical journal PY - 1983 SP - 131 EP - 132 VL - 24 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S001708950000519X/ DO - 10.1017/S001708950000519X ID - 10_1017_S001708950000519X ER -
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