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.

In this paper, the concept of Semi-group in multiset context is introduced. The condition for a sub semi-multigroup to be established and study closure operationson class finite semi-multigroups carried out.Commutative andcancellative properties operations on are studied. We also studiedthe commutative cancellative semi-multigroups.

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...

A family of subsets of an n-set is 2-cancellative if for every four-tuple {A, B, C, D} of its members A ∪B ∪C = A ∪B ∪D implies C = D. This generalizes the concept of cancellative set families, defined by the property that A ∪B 6= A ∪C for A, B, C all different. The asymptotics of the maximum size of cancellative families of subsets of an n-set is known, (Tolhuizen [7]). We provide a new upper ...

We give a characterization of primary ideals of finitely generated commutative monoids and in the case of finitely generated cancellative monoids we give an algorithmic method for deciding if an ideal is primary or not. Finally we give some properties of primary elements of a cancellative monoid and an algorithmic method for determining the primary elements of a finitely generated cancellative ...

Quasi-cancellativity is the generalization of cancellativity. We introduce the notion of quasi-cancellativity of semigroup into AG-groupoids. We prove that every AG-band is quasi-cancellative. We also prove the famous Burmistrovich’s Theorem for AG-groupoids that states “An AG∗∗-groupoid S is a quasi-cancellative if and only if S is a semilattice of cancellative AG∗∗-groupoids”.

The structure of cancellative t-norms is studied. It is shown that a cancellative tnorm is generated if and only if it has no anomalous pair, and then it is Archimedean. Moreover, if it is also continuous in point (1,1) it is isomorphic to the product tnorm. Several examples of non-generated cancellative t-norms are also given.

A triple system is cancellative if no three of its distinct edges satisfy A ∪ B = A ∪ C. It is tripartite if it has a vertex partition into three parts such that every edge has exactly one point in each part. It is easy to see that every tripartite triple system is cancellative. We prove that almost all cancellative triple systems with vertex set [n] are tripartite. This sharpens a theorem of N...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.