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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1148,
author = {Ivan Chajda and Miroslav Kola\v r\'\i k},
title = {Remarks on pseudo MV-algebras},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {29},
year = {2009},
pages = {5-19},
zbl = {1194.06006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1148}
}
Ivan Chajda; Miroslav Kolařík. Remarks on pseudo MV-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 29 (2009) pp. 5-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1148/
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