Dvurečenskij, Anatolij Pseudo MV-algebras are intervals in \(\ell\)-groups. (English) Zbl 1027.06014 J. Aust. Math. Soc. 72, No. 3, 427-445 (2002). Pseudo MV-algebras were introduced by G. Georgescu and A. Iorgulescu [Mult.-Valued Log. 6, 95-135 (2001; Zbl 1014.06008)] as natural noncommutative generalization of MV-algebras. The author proves that pseudo MV-algebras are categorically equivalent to lattice-ordered groups (not necessarily abelian) with a strong unit, so extending a famous result of D. Mundici [J. Funct. Anal. 65, 15-63 (1986; Zbl 0597.46059)]. Reviewer: Salvatore Sessa (Napoli) Cited in 9 ReviewsCited in 130 Documents MSC: 06D35 MV-algebras 06F15 Ordered groups Keywords:pseudo MV-algebra; categorical equivalence; lattice-ordered groups PDF BibTeX XML Cite \textit{A. Dvurečenskij}, J. Aust. Math. Soc. 72, No. 3, 427--445 (2002; Zbl 1027.06014) Full Text: DOI OpenURL References: [1] Darnel, Theory of lattice-ordered groups (1995) · Zbl 0810.06016 [2] Dvurečenskij, Proc. Fourth Inter Symp. on Econ. Inform., May 6–9, 1999, Bucharest pp 952– (1999) [3] DOI: 10.2307/1993227 · Zbl 0084.00704 [4] DOI: 10.1007/BF01234363 · Zbl 0472.06028 [5] Birkhoff, Lattice theory (1997) [6] DOI: 10.2307/2372361 · Zbl 0033.34504 [7] Wyler, Compos. Math. 17 pp 172– (1966) [8] DOI: 10.1007/BF01900297 · Zbl 0073.03801 [9] DOI: 10.1016/0022-1236(86)90015-7 · Zbl 0597.46059 [10] MacLane, Categories for the working mathematician (1971) [11] Höhle, Non-classical logic and their representation to fuzzy subsets pp 53– (1995) [12] Georgescu, Mult.-Valued Log. 6 pp 95– (2001) [13] Dvurečenskij, New trends in quantum structures (2000) [14] Fuchs, Partially ordered algebraic systems (1963) · Zbl 0137.02001 [15] Dvurečenskij, Tatra Mt. Math. Publ. 15 pp 31– (1998) [16] Cignoli, Algebraic foundations of many-valued reasoning (2000) · Zbl 0937.06009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.