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An elementary presentation of the equivalence between MV-algebras and \(\ell\)-groups with strong unit. (English) Zbl 0964.06009

The well-known functor \(\Gamma\) is a basic tool for investigating the relations between MV-algebras and lattice-ordered groups. The second author [J. Funct. Anal. 65, 15-63 (1986; Zbl 0597.46059)] proved that \(\Gamma\) is a natural equivalence between the category of MV-algebras and the category of abelian lattice-ordered groups with strong units.
The main novelty of the method given in the present paper can be characterized as follows. The authors show that Chang’s construction [C. C. Chang, Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704); ibid. 93, 74-80 (1959; Zbl 0093.01104)] of the enveloping group \(G_A\) starting from a linearly ordered MV-algebra \(A\) can be generalized to the case of any MV-algebra \(A\).
This important paper deserves to be read by all people working in the field of MV-algebras.

MSC:

06D35 MV-algebras
06F15 Ordered groups
03G25 Other algebras related to logic
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