A note on generators of the endomorphism semigroup of an infinite countable chain

Ilinka Dimitrova, Vitor H. Fernandes, Joerg Koppitz

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Abstract

In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.
Original languageEnglish
Article number 1750031
JournalJOURNAL OF ALGEBRA AND ITS APPLICATIONS
Volume16
Issue number2
DOIs
Publication statusPublished - Feb 2017

Keywords

  • Infinite chain
  • endomorphism semigroup
  • generators
  • relative rank

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