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algebra universalis

, Volume 39, Issue 3–4, pp 163–169 | Cite as

Some equivalents of AC in algebra II

  • K. Keremedis
  • 43 Downloads

Abstract.

We show that the axiom of choice AC is equivalent to the statement Any quotient group of any abelian group has a selector. We also show that the multiple choice axiom MC is equivalent to the assertion: Any filter \( \cal F \) in any Boolean ring \( B, + , \bullet \) has a well ordered filterbase.

Key words and phrases: Axiom of choice, quotient group, Boolean ring, filter. 

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Copyright information

© Birkhäuser Verlag Basel, 1998

Authors and Affiliations

  • K. Keremedis
    • 1
  1. 1.Department of Mathematics, University of the Aegean, GR-83200 Karlovasi, Samos, Greece. E-mail: kker@aegean.grGR

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