Geodesic
Negation in bounded commutative $DR\ell$-monoids
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 755-763

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The class of commutative dually residuated lattice ordered monoids ($DR\ell $-monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras. In the paper, a unary operation of negation in bounded $DR\ell $-monoids is introduced, its properties are studied and the sets of regular and dense elements of $DR\ell $-monoids are described.
Classification : 06D35, 06F05
Keywords: $DR\ell $-monoid; $MV$-algebra; $BL$-algebra; Brouwerian algebra; negation 
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     author = {Rach\r{u}nek, Ji\v{r}{\'\i} and Slez\'ak, Vladim{\'\i}r},
     title = {Negation in bounded commutative $DR\ell$-monoids},
     journal = {Czechoslovak Mathematical Journal},
     pages = {755--763},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2006},
     mrnumber = {2291772},
     zbl = {1164.06325},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006__56_2_a36/}
}
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Rachůnek, Jiří; Slezák, Vladimír. Negation in bounded commutative $DR\ell$-monoids. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 755-763. http://geodesic.mathdoc.fr/item/CMJ_2006__56_2_a36/