The Hahn Embedding Theorem for a Class of Residuated Semigroups

Structure Theorem for a Class of Group-like Residuated Chains à la Hahn

Hahn’s famous structure theorem states that totally ordered Abelian groups can be embedded in the lexicographic product of real groups. Our main theorem extends this structural description to order-dense, commutative, group-like residuated chains, which has only finitely many idempotents. It is achieved via the so-called partial-lexicographic product construction (to be introduced here) using t...

The Hahn Embedding Theorem for Abelian Lattice-ordered Groups

A FUZZY VERSION OF HAHN-BANACH EXTENSION THEOREM

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

The equational theories of representable residuated semigroups

We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.

On representable ordered residuated semigroups

We show that the equational theory of representable lattice-ordered residuated semigroups is not finitely axiomatizable. We apply this result to the problem of completeness of substructural logics.