On Algebras Based on Representable Uninorms
Enrico Marchioni · 2015
Representable uninorms form a spe-cial class of uninorms that have an additive generator over the whole real line bounded by −∞,+∞. Al-gebras based on left-continuous and conjunctive representable uninorms, called RU-algebras, form a subvari-ety of commutative bounded residu-ated lattices, and are strictly related to Abelian `-groups. In this work, we study this rela-tion by showing that the category of Abelian `-groups is equivalent to a full subcategory of RU-algebras. Moreover we prove that the variety of RU-algebras is generated by ev-ery single infinite RU-chain. Finally, we briefly study some simple model-theoretic properties of the class of RU-chains that are related to or-dered divisible Abelian groups.