PROCEEDINGS IPMU '08

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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