Skip to main content Accessibility help
×
×
Home

Unique factorization in Cayley arithmetics and cryptology

  • P. J. C. Lamont (a1)
Extract

Let be the classical Cayley algebra defined over the reals with basis where gives a quaternion algebra ℋ4 with i0 = 1, i1i2i3 = −1, i1i4 = i5, i2i4 = i6 and i3i4 = i7. The multiplication table of the imaginary basic units follows:

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Unique factorization in Cayley arithmetics and cryptology
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Unique factorization in Cayley arithmetics and cryptology
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Unique factorization in Cayley arithmetics and cryptology
      Available formats
      ×
Copyright
References
Hide All
1.van der Blij, F., History of the octaves, Simon Stevin 34 (1961), 106125.
2.van der Blij, F. and Springer, T. A., The arithmetics of the octaves and of the group G2, Nederl. Akad. Wetensch. Proc. (=Indag. Math.) 62A (1959), 406418.
3.Dickson, L. E., On quaternions and their generalization and the history of the eight square theorem, Annals of Math. (2), 20 (1919), 155171, 297.
4.Hurwitz, A., Über die Composition der quadratischen Formen von beliebig vielen Variabeln, Nachr. Gesell. Wiss. Göttingen (1898), 309316.
5.Lamont, P. J. C., Arithmetics in Cayley's algebra, Proc. Glasgow Math. Assoc. 6 (1963), 99106.
6.Lamont, P. J. C., Ideals in Cayley's algebra, Nederl. Akad. Wetensch. Proc. (= Indag. Math.) 66A (1963), 394400.
7.Lamont, P. J. C., Approximation theorems for the group G2, Nederl. Akad. Wetensch. Proc. (=Indag. Math.) 67A (1964), 187192.
8.Lamont, P. J. C., Factorization and arithmetic functions for orders in composition algebras, Glasgow Math. J. 14 (1973), 8695.
9.Lamont, P. J. C., The number of Cayley integers of given norm, Proc. Edinburgh Math. Soc. 25 (1982), 101103.
10.Lamont, P. J. C., Computer generated natural inner automorphisms of Cayley's algebra, Glasgow Math. J. 23 (1982), 187189.
11.Lamont, P. J. C., The nonexistence of a factorization formula for Cayley numbers, Glasgow Math. J. 24 (1983), 131132.
12.Rankin, R. A., On representations of a number as a sum of squares and certain related identities, Proc. Camb. Phil. Soc. 41 (1945), 111.
13.Rankin, R. A., A certain class of multiplicative functions, Duke Math. J. 13 (1946), 281306.
14.Taussky, O., Sums of squares, Amer. Math. Monthly 77 (1970), 805830.
15.Welsh, D., Codes and Cryptography (Oxford, 1988).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed