Algebra universalis

, Volume 71, Issue 2, pp 191–200 | Cite as

Projective objects in the categories of abelian -groups and MV-algebras



We provide a description of free MV-algebras as subalgebras of intervals of free Abelian -groups. This description shows that the unital Abelian -group corresponding to a free MV-algebra is projective as an Abelian -group. More generally, we prove that this is still the case for projective MV-algebras. Using a construction similar to the one for MV-algebras, we show that the free algebras in the variety of negative cones of Abelian -groups are subalgebras of negative cones of free Abelian -groups. This allows us to prove a Baker–Beynon-type theorem for finitely generated free algebras in the variety of negative cones of Abelian -groups. These results are specific cases of a more general situation, which is the subject of the last section of this paper.

2010 Mathematics Subject Classification

Primary: 06F15 Secondary: 06D35 

Key words and phrases

-groups MV-algebras negative cones projective 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsVanderbilt UniversityNashvilleU.S.A

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