# Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures

In: Mathematica Slovaca, vol. 56, no. 2
Dually residuated lattice ordered monoids ($DR\ell$-monoids) form a large class that contains among others all lattice ordered groups, fuzzy structures which need not be commutative, for instance, pseudo $BL$-algebras and $GMV$-algebras (= pseudo $MV$-algebras) and Brouwerian algebras. In the paper, two concepts of negation in bounded $DR\ell$-monoids are introduced and their properties are studied in general as well as in the case of the so-called good $DR\ell$-monoids. The sets of regular and dense elements of good $DR\ell$-monoids are described.