A P–THEOREM FOR ORDERED GROUPOIDS
N. D. Gilbert · 2007
McAlister’s P-theorem for E–unitary inverse semigroups is one of the most significant components of the structure theory for inverse semigroups: since its first appearance in 1974 several different proofs have been given and the scope of the theorem has been extended to strongly E∗–unitary and strongly categorical inverse semigroups. In this paper, we prove a P–theorem for the wider class of incompressible ordered groupoids, which encompasses previous versions of the P–theorem and offers a unified proof. Moreover, the class of incompressible ordered groupoids may be of interest in its own right, and we look at examples related to Bass-Serre theory for groups.