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.
 | PDF full paper |