Leonardo Manuel Cabrer

RATIONAL POLYHEDRA AND PROJECTIVE LATTICE-ORDERED ABELIAN GROUPS WITH ORDER UNIT

An l-group G is an abelian group equipped with a translation invariant lattice order. Baker and Beynon proved that G is finitely generated projective iff it is finitely presented. A unital l-group is an l-group G with a distinguished order unit, i.e., an element u in G whose positive integer multiples eventually dominate every element of G. While every finitely generated projective unital l-group is finitely presented, the converse does not hold in general. Classical algebraic topology (a la Whitehead) will be combined in this paper with the W{\l}odarczyk-Morelli solution of the weak Oda conjecture for toric varieties, to describe finitely generated projective unital l-groups.

Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras ∗

In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.

Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups

Abstract. A unital

A Stone–Weierstrass theorem for MV-algebras and unital ℓ-groups

\ell

Classifying orbits of the affine group over the integers

-group (G,u)

A general framework for product representations: bilattices and beyond

(G,u)

MV-algebras, infinite dimensional polyhedra, and natural dualities

is an abelian group G

Polyhedral MV-algebras

G

Unification and Projectivity in De Morgan and Kleene Algebras

equipped with a translation-invariant lattice-order and a distinguished element u

MV-algebras freely generated by finite Kleene algebras

u