Interior and closure operators on bounded residuated lattice ordered monoids

GMV-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior GMV-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on DRl-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on GMV-algebras.