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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 $-monoids are described.
The class of commutative dually residuated lattice ordered monoids ($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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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/

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