Geodesic
Remarks on pseudo MV-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 5-19.

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Pseudo MV-algebras (see e.g., [4, 6, 8]) are non-commutative extension of MV-algebras. We show that every pseudo MV-algebra is isomorphic to the algebra of action functions where the binary operation is function composition, zero is x ∧ y and unit is x. Then we define the so-called difference functions in pseudo MV-algebras and show how a pseudo MV-algebra can be reconstructed by them.
Keywords: pseudo MV-algebra, action function, guard function, difference functions 
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Chajda, Ivan; Kolařík, Miroslav. Remarks on pseudo MV-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_1_a0/

[1] S.L. Bloom, Z. Ésik and E. Manes, A Cayley theorem for Boolean algebras, Amer. Math. Monthly 97 (1990), 831-833.

[2] I. Chajda, A representation of the algebra of quasiordered logic by binary functions, Demonstratio Mathem. 27 (1994), 601-607.

[3] I. Chajda and H. Länger, Action algebras, Italian J. of Pure Appl. Mathem., submitted.

[4] I. Chajda and J. Kühr, Pseudo MV-algebras and meet-semilattices with sectionally antitone permutations, Math. Slovaca 56 (2006), 275-288.

[5] A. Dvurečenskij, Pseudo MV-algebras are intervals in l-groups, J. Aust. Math. Soc. 72 (3) (2002), 427-445.

[6] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated Lattices, An Algebraic Glimpse at Substructural Logics, Elsevier 2007.

[7] G. Georgescu and A. Iorgelescu, Pseudo MV-algebras, Multiple Valued Log. 6 (2001), 95-135.

[8] A.M.W Glass and W.C. Holland, Lattice-Ordered Groups, Kluwer Acad. Publ., Dordrecht-Boston-London 1989.

[9] P. Jipsen and C. Tsinakis, A survey of Residuated Lattices, Ordered Agebraic Structures (Martinez J., editor), Kluwer Academic Publishers, Dordrecht, 2002, 19-56.

[10] J. Kühr and F. Švrček, Operators on unital l-groups, preprint, 2007.

[11] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273.