Arithmetic and other properties of certain Delphic semigroups. I

  • Rollo Davidson


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.


Stochastic Process Probability Theory Mathematical Biology Aboriginal Element Canonical Factorization 


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Copyright information

© Springer-Verlag 1968

Authors and Affiliations

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

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