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