Abstract
We consider a non-associative generalization of MV-algebras. The underlying posets of our non-associative MV-algebras are not lattices, but they are related to so-called λ-lattices.

Editor-in-Chief: Pulmannová, Sylvia
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We consider a non-associative generalization of MV-algebras. The underlying posets of our non-associative MV-algebras are not lattices, but they are related to so-called λ-lattices.
Keywords: MV-algebra; λ-lattice
[1] ABBOTT, J. C.: Semi-boolean algebra, Mat. Vesnik 4 (1967), 177–198. Google Scholar
[2] BAHLS, P.—COLE, — J. GALATOS, — N. JIPSEN, — P. TSINAKIS, C.: Cancellative residuated lattices, Algebra Universalis 50 (2003), 83–106. http://dx.doi.org/10.1007/s00012-003-1822-4CrossrefGoogle Scholar
[3] CHAJDA, I. — HALAŠ, — R. KÜHR, J.: Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19–33. Google Scholar
[4] CHAJDA, I. — HALAŠ, R. — KÜHR, J.: Implication in MV-algebras, Algebra Universalis 52 (2004), 377–382. http://dx.doi.org/10.1007/s00012-004-1862-4CrossrefWeb of ScienceGoogle Scholar
[5] CHANG, C. C.: Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc. 88 (1958), 467–490. http://dx.doi.org/10.2307/1993227CrossrefGoogle Scholar
[6] CHANG, C. C.: A new proof of the completeness of the Łukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74–80. http://dx.doi.org/10.2307/1993423CrossrefGoogle Scholar
[7] CIGNOLI, R. L. O. — D’OTTAVIANO, I. M. L. — MUNDICI, D.: Algebraic Foundations of Many-valued Reasoning, Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. Google Scholar
[8] GALATOS, N. — TSINAKIS, C.: Generalized MV-algebras, J. Algebra 283 (2005), 254–291. http://dx.doi.org/10.1016/j.jalgebra.2004.07.002CrossrefGoogle Scholar
[9] GEORGESCU, G. — IORGULESCU, A.: Pseudo-MV algebras, Mult.-Valued Log. 6 (2001), 95–135. Google Scholar
[10] JEŽEK, J. — QUACKENBUSH, R.: Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49–69. http://dx.doi.org/10.1007/BF01190253CrossrefGoogle Scholar
[11] KARÁSEK, J.: Rotations of λ-lattices, Math. Bohem. 121 (1996), 293–300. Google Scholar
[12] MANGANI, P.: Su certe algebre connesse con logiche a piú valori, Boll. Unione Mat. Ital. Ser. IV. 8 (1973), 68–78. Google Scholar
[13] MUNDICI, D.: Interpretation of AF C*-algebras in Łukasiewicz sentential calculus, J. Funct. Anal. 65 (1986), 15–63. http://dx.doi.org/10.1016/0022-1236(86)90015-7CrossrefGoogle Scholar
[14] RACHŮNEK, J.: A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255–273. http://dx.doi.org/10.1023/A:1021766309509CrossrefGoogle Scholar
[15] SNÁŠEL, V.: λ-lattices. Ph.D. Thesis, Masaryk Univ., Brno, 1991. Google Scholar
[16] SNÁŠEL, V.: λ-lattices, Math. Bohem. 122 (1997), 267–272. Google Scholar
Published Online: 2007-08-01
Published in Print: 2007-08-01
Citation Information: Mathematica Slovaca, Volume 57, Issue 4, Pages 301–312, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-007-0024-5.
© 2007 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0
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