• Published 2004

Beyond ideals in the Dickson ring of integral octonions

@inproceedings{ChaitinChatelin2004BeyondII,
  title={Beyond ideals in the Dickson ring of integral octonions},
  author={Françoise Chaitin-Chatelin},
  year={2004}
}
This is ongoing work on hypercomputation [4]. We revisit the works of Dickson [5] and Mahler [9] on integral octonions. Nonassociativity (in the form of alternativity) leads to the unexpected consequence that the theorem of (at most) 4 squares (Bachet – Lagrange) becomes a theorem of (exactly) 1, 2 or 4 identical squares for a subset of N∗. These numbers measure the norm of the vectors in the Dickson ring of integral octonions for which the associator (with 3 or 7 pairs of distinct imaginary… CONTINUE READING

Figures from this paper.

References

Publications referenced by this paper.
SHOWING 1-9 OF 9 REFERENCES

The Octonions

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Ideals in cayley’s algebra

VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

On ideals in the Cayley – Dickson algebra

  • K. Mahler
  • Proc. Royal Irish Acad
  • 1942
VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

A new simple theory of hypercomplex integers

  • L. E. Dickson
  • J. de Math. Pures et Appl
  • 1923
VIEW 14 EXCERPTS
HIGHLY INFLUENTIAL

Vorlesungen über die Zahlentheorie der Quaternionen

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Ideals in the Integral Octaves

VIEW 3 EXCERPTS