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algebra universalis

, Volume 50, Issue 1, pp 61–67 | Cite as

On generating countable sets of endomorphisms

  • J. Araújo
  • J. D. Mitchell
  • N. Silva
Original Paper

Abstract.

Sierpiński proved that every countable set of mappings on an infinite set X is contained in a 2-generated subsemigroup of the semigroup of all mappings on X. In this paper we prove that every countable set of endomorphisms of an algebra \( \mathcal{A} \) which has an infinite basis (independent generating set) is contained in a 2-generated subsemigroup of the semigroup of all endomorphisms of \( \mathcal{A} \).

Mathematics Subject Classification (2000):

20M20, 20M10, 08A35. 
Keywords: Endomorphisms universal algebras independence semigroups 

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Copyright information

© Birkhäuser-Verlag Basel 2003

Authors and Affiliations

  1. 1.R. Escola Politécnica, 147Universidade AbertaLisboaPortugal
  2. 2.Centro de ÁlgebraUniversidade de LisboaLisboaPortugal
  3. 3.Mathematics InstituteUniversity of St AndrewsSt Andrews, FifeUK

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