HNN extensions of inverse semigroups with zero

E. R. Dombi; N. D. Gilbert

doi:10.1017/S0305004106009856

HNN extensions of inverse semigroups with zero

E. R. Dombi, N. D. Gilbert

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2 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	25-39
Number of pages	15
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	142
Issue number	1
DOIs	https://doi.org/10.1017/S0305004106009856
Publication status	Published - Jan 2007

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AB - 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.

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HNN extensions of inverse semigroups with zero

Abstract

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