Irreducible semigroups

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 ...

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.

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.

Pacific Journal of Mathematics IRREDUCIBLE NUMERICAL SEMIGROUPS

Irreducible Matrix Representations of Finite Semigroups

Munn [9] has shown that for a semigroup S satisfying the minimal condition on principal ideals, there is a natural one-to-one correspondence between irreducible representations of S and irreducible representations vanishing at zero of its 0-simple (or simple) principal factors; for the case of S finite, see Ponizovskii [11]. On the other hand, Clifford, [3] and [4], has obtained all representat...