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CAYLEY--DICKSON SPLIT-ALGEBRAS: DOUBLY ALTERNATIVE ZERO DIVISORS AND RELATION GRAPHS
- Source :
- Journal of Mathematical Sciences. January 4, 2023, Vol. 269 Issue 3, p331, 25 p.
- Publication Year :
- 2023
-
Abstract
- 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. To the memory of V. T. Markov<br />1. Introduction The zero divisors of the Cayley--Dickson algebras are of special interest; however, the problem of their identification and description of their annihilators is rather difficult. Some attempts to [...]
- Subjects :
- Algebra
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 269
- Issue :
- 3
- Database :
- Gale General OneFile
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- edsgcl.742001985
- Full Text :
- https://doi.org/10.1007/s10958-023-06285-5