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Keywords:
$DR\ell$-monoid; $MV$-algebra; $BL$-algebra; Brouwerian algebra; negation
Summary:
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.
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