This paper is dedicated to study dense left cancellative languages.A characterization and some important properties of this class of languages ia given by using some class of semi-singular words.

We introduce the concept of presentation for the Archimedean components of finitely generated commutative monoids. Some properties like being cancellative, torsion freeness and separativity are studied under this new point of view.

Let M be a commutative cancellative atomic monoid. We use unions of sets of lengths in M to construct the V-Delta set of M . We first derive some basic properties of V-Delta sets and then show how they offer a method to investigate the asymptotic behavior of the sizes of unions of sets of lengths. A central focus of number theory is the study of number theoretic functions and their asymptotic b...

Our work proposes a new paradigm for the study of various classes of cancellative residuated lattices by viewing these structures as lattice-ordered groups with a suitable operator (a conucleus). One consequence of our approach is the categorical equivalence between the variety of cancellative commutative residuated lattices and the category of abelian lattice-ordered groups endowed with a conu...