AI 中文总结
该研究探讨实Cayley-Dickson代数的正交图，构造定向六边形，确定双六边形顶点乘法表，给出生成交错子代数的条件，分类特定零因子并明确其正交条件。
AI 中文摘要
我们研究两两强交错的分量构成的零因子，并在任意实Cayley-Dickson代数的零因子图中构造定向六边形。对于主序列代数，零因子图与正交图重合，且任意六边形均可扩展为双六边形。我们确定双六边形顶点的乘法表，接着给出三个元素生成任意Cayley-Dickson代数交错子代数的充分条件。最后，我们考虑分量为标准基元素（带符号）的零因子，对其分类并确定其中两个元素正交的充要条件。
英文摘要
We study zero divisors whose components alternate strongly pairwise and construct oriented hexagons in the zero divisor graph of an arbitrary real Cayley-Dickson algebra. In case of the algebras of the main sequence, the zero divisor graph coincides with the orthogonality graph, and any hexagon can be extended to a double hexagon. We determine the multiplication table of the vertices of a double hexagon. Then we find a sufficient condition for three elements to generate an alternative subalgebra of an arbitrary Cayley-Dickson algebra. Finally, we consider those zero divisors whose components are both standard basis elements up to sign. We classify them and determine necessary and sufficient conditions under which two such elements are orthogonal.
Journal refS. Zhilina, Orthogonality graphs of real Cayley-Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons, Int. J. Algebra Comput. 31(4) (2021) 663-689
