TY - JOUR
T1 - Cayley–Dickson Split-Algebras
T2 - Doubly Alternative Zero Divisors and Relation Graphs
AU - Guterman, A. E.
AU - Zhilina, S. A.
N1 - Publisher Copyright:
© 2023, Springer Nature Switzerland AG.
PY - 2023/1
Y1 - 2023/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85148503034&partnerID=8YFLogxK
U2 - 10.1007/s10958-023-06285-5
DO - 10.1007/s10958-023-06285-5
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AN - SCOPUS:85148503034
SN - 1072-3374
VL - 269
SP - 331
EP - 355
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 3
ER -