On Algebras Based on Representable Uninorms

Enrico Marchioni.

Representable uninorms form a special class of uninorms that have an additive generator over the whole real line bounded by -∞,+∞. Algebras based on left-continuous and conjunctive representable uninorms, called RU-algebras, form a subvariety of commutative bounded residuated lattices, and are strictly related to Abelian l-groups. In this work, we study this relation by showing that the category of Abelian l-groups is equivalent to a full subcategory of RU-algebras. Moreover we prove that the variety of RU-algebras is generated by every single infinite RU-chain. Finally, we briefly study some simple modeltheoretic properties of the class of RU-chains that are related to ordered divisible Abelian groups.

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