On bisimple weakly inverse semigroups

Semilattice of Bisimple Regular Semigroups

The main purpose of this paper is to show that a regular semigroup S is a semilattice of bisimple semigroups if and only if it is a band of bisimple semigroups and that this holds if and only if 3) is a congruence on S. It is also shown that a quasiregular semigroup 5 which is a rectangular band of bisimple semigroups is itself bisimple. In [3, Theorem 4.4] it was shown that a semigroup S is a ...

Partial Actions of Inverse and Weakly Left E-ample Semigroups

We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation α 7→ α, where α is the identity map on the domain of α. We investigate t...

Primer on Inverse Semigroups

Inverse Semigroups Acting on Graphs

There has been much work done recently on the action of semigroups on sets with some important applications to, for example, the theory and structure of semigroup amalgams. It seems natural to consider the actions of semigroups on sets ‘with structure’ and in particular on graphs and trees. The theory of group actions has proved a powerful tool in combinatorial group theory and it is reasonable...

A Note on Amalgams of Inverse Semigroups