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

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Abstract

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

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  1. Department of Mathematics, Vanderbilt University, Nashville, U.S.A

    William Young

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  1. William Young
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Correspondence to William Young.

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Presented by J. Raftery.

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Young, W. Projective objects in the categories of abelian ℓ-groups and MV-algebras. Algebra Univers. 71, 191–200 (2014). https://doi.org/10.1007/s00012-014-0268-1

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  • DOI: https://doi.org/10.1007/s00012-014-0268-1

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