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/