Abstract
The classical Hurwitz theorem claims that there are exactly four normed algebras with division: the real numbers (R), complex numbers (C), quaternions(H), and octonions (O). The length of R as an algebra over itself is zero; the length of C as an R-algebra equals one. The purpose of the present paper is to prove that the lengths of the R-algebras of quaternions and octonions equal two and three, respectively.
Original language | English |
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Pages (from-to) | 826-832 |
Number of pages | 7 |
Journal | Journal of Mathematical Sciences |
Volume | 224 |
Issue number | 6 |
DOIs | |
State | Published - Aug 2017 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Statistics and Probability
- General Mathematics