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Arithmetic and other properties of certain Delphic semigroups. I

  • Rollo Davidson
Article

Summary

Some aspects of Delphic semigroups in general — in particular, the idea of an hereditary subsemigroup, which has many uses in connexion with Delphic semigroups — are first treated. After that, attention is directed to the arithmetic of ℛ+, the semigroup of positive renewal sequences. In a Delphic semigroup the aboriginal elements are the ‘simples’ and the members of ‘I0’: a class of simples of ℛ+ is constructed and the simples are shown to be residual. I0 is explicitly identified, and this leads to a canonical factorization of ℛ+. The properties of division in ℛ+ are discussed.

Keywords

Stochastic Process Probability Theory Mathematical Biology Aboriginal Element Canonical Factorization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • Rollo Davidson
    • 1
  1. 1.Trinity CollegeCambridgeGreat Britain

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