On left restriction semigroups with zero

Abstract EN

In this article, we give the notion of left restriction meet-semigroup, and establish some results regarding atomistic left restriction semigroups.

Then we discuss decompositions of (non-zero) semigroups with zero by proving a decomposition theorem.

We also show that every atomistic left restriction semigroup S can be decomposed as an orthogonal sum of atomistic left restriction semigroups Ni , where each summand Ni is an irreducible ideal of S.

Finally, properties of the summands Ni , when S embeds in some PT X the partial transformation monoid on a set X, are investigated.