Cignoli, Roberto; Mundici, Daniele An elementary presentation of the equivalence between MV-algebras and \(\ell\)-groups with strong unit. (English) Zbl 0964.06009 Stud. Log. 61, No. 1, 49-64 (1998). 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. Reviewer: Jan Jakubík (Košice) Cited in 9 Documents MSC: 06D35 MV-algebras 06F15 Ordered groups 03G25 Other algebras related to logic Keywords:MV-algebra; abelian lattice ordered group; functor \(\Gamma\); natural equivalence Citations:Zbl 0084.00704; Zbl 0093.01104; Zbl 0597.46059 PDFBibTeX XMLCite \textit{R. Cignoli} and \textit{D. Mundici}, Stud. Log. 61, No. 1, 49--64 (1998; Zbl 0964.06009) Full Text: DOI