Pseudo-MV Algebras as L-algebras
Yichuan Yang and Wolfgang Rump
Pseudo-MV algebras are viewed as an algebraic framework of “noncommutative” reasoning with two negations. In this paper, we observe that pseudo-MV algebras can be described as monoids with a single negation. This leads to a characterization of pseudo-MV algebras as semiregular L-algebras with negation, especially, the proof neither makes use of the self-similar closure, nor of l-group interval representation. As an application, a new proof of Dvurecenskij’s representation theorem for pseudo-MV algebras is obtained.
Keywords: L-algebra, left hoop, pseudo MV-algebra, brick
2010 Mathematics Subject Classification. Primary: 06F15, 06F05, 03G25.