Heriot-Watt Mathematics Report Series
HWM05-36, 30 Mar 2006

A P-theorem for ordered groupoids

N D Gilbert


Abstract

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.

Google Scholar Search: links, citations and journal (if available)


Contact Details | 2005 Reports Index | Full Index