The Classification of All the Subvarieties of DNMG

MTL is the logic of all left-continuous t-norms and their residua. The equivalent algebraic semantics of MTL is constituted by the variety of MTL-algebras, MTL. The variety WNM of weak nilpotent minimum algebras is a major subvariety of MTL, containing several subvarieties of MTL which have been subjects of study in the literature, such as Godel algebras, Nilpotent Minimum algebras, Drastic Product and Revised Drastic Product algebras, NMG-algebras, as well as Boolean algebras. In this paper we introduce and axiomatise DNMG, a proper subvariety of WNM which contains all the aforementioned varieties. We show that DNMG is singly generated by a standard algebra. Further, we determine the structure of the lattice of subvarieties of DNMG, and we provide the axiomatisation of every subvariety.