Heriot-Watt Mathematics Report Series
HWM05-36, 30 Mar 2006
A P-theorem for ordered groupoids
N D Gilbert
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.
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