Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of, e.g., $BL$-algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative $R\ell $-monoids are investigated.
The class of commutative dually residuated lattice ordered monoids ($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.