Cayley--Dickson split-algebras: Doubly alternative zero divisors and relation graphs
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 95-129
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Our paper is devoted to the investigations of doubly alternative zero divisors of the real Cayley–Dickson split-algebras. We describe their annihilators and orthogonalizers and also establish the relationship between centralizers and orthogonalizers for such elements. Then we obtain an analogue of the real Jordan normal form in the case of the split-octonions. Finally, we describe commutativity, orthogonality, and zero divisor graphs of the split-complex numbers, the split-quaternions, and the split-octonions in terms of their diameters and cliques.
@article{FPM_2020_23_3_a7,
author = {A. E. Guterman and S. A. Zhilina},
title = {Cayley--Dickson split-algebras: {Doubly} alternative zero divisors and relation graphs},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {95--129},
publisher = {mathdoc},
volume = {23},
number = {3},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a7/}
}
TY - JOUR AU - A. E. Guterman AU - S. A. Zhilina TI - Cayley--Dickson split-algebras: Doubly alternative zero divisors and relation graphs JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2020 SP - 95 EP - 129 VL - 23 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a7/ LA - ru ID - FPM_2020_23_3_a7 ER -
%0 Journal Article %A A. E. Guterman %A S. A. Zhilina %T Cayley--Dickson split-algebras: Doubly alternative zero divisors and relation graphs %J Fundamentalʹnaâ i prikladnaâ matematika %D 2020 %P 95-129 %V 23 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a7/ %G ru %F FPM_2020_23_3_a7
A. E. Guterman; S. A. Zhilina. Cayley--Dickson split-algebras: Doubly alternative zero divisors and relation graphs. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 95-129. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a7/