Cayley–Dickson Split-Algebras: Doubly Alternative Zero Divisors and Relation Graphs

A. E. Guterman, S. A. Zhilina

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)331-355
Number of pages25
JournalJournal of Mathematical Sciences
Issue number3
StatePublished - Jan 2023
Externally publishedYes

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