Irreducible numerical semigroups

Irreducible Numerical Semigroups

We give a characterization for irreducible numerical semi-groups. From this characterization we obtain that every irre-ducible numerical semigroup is either a symmetric or pseudo-symmetric numerical semigroup. We study the minimal presentations of an irreducible numerical semigroup. Separately, we deal with the cases of maximal embedding dimension and multiplicity 3 and 4.

Pacific Journal of Mathematics IRREDUCIBLE NUMERICAL SEMIGROUPS

Irreducible Numerical Semigroups Having Toms Decomposition

In this paper we prove that if S is an irreducible numerical semigroup and S is generated by an interval or S has multiplicity 3 or 4, then it enjoys Toms decomposition. We also prove that if a numerical semigroup can be expressed as an expansion of a numerical semigroup generated by an interval, then it is irreducible and has Toms decomposition.

Join irreducible semigroups

We begin a systematic study of those finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral theory of this lattice. Finite semigroups S that generate join irreducible pseudovari-eties are characterized as follows: whenever S divides a direct product A × B of finite semigroups, then S divides either A ...

Subdirectly irreducible acts over some semigroups

‎In this paper‎, ‎we characterize and find the number of subdirectly‎ ‎irreducible acts over some classes of semigroups‎, ‎such as zero‎ ‎semigroups‎, ‎right zero semigroups‎ ‎and strong chain of left zero semigroups.