HNN extensions of inverse semigroups with zero

E. R. Dombi, N. D. Gilbert

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We study a construction of an HNN extension for inverse semigroups with zero. We prove a normal form for the elements of the universal group of an inverse semigroup that is categorical at zero, and use it to establish structural results for the universal group of an HNN extension. Our main application of the HNN construction is to show that graph inverse semigroups - including the polycyclic monoids - admit HNN decompositions in a natural way, and that this leads to concise presentations for them. © 2007 Cambridge Philosophical Society.

Original languageEnglish
Pages (from-to)25-39
Number of pages15
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
Publication statusPublished - Jan 2007


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