A triple [S,T;U] where S and T are inverse semigroups and U is the intersection of S and T is called an amalgam of inverse semigroups. The amalgamated free product associated to the amalgam [S,T;U] is defined by the usual universal diagram and it is well-known that each amalgams of inverse semigroups embeds in its associated aalgamated free product. In general amalgamated free products of inverse semigroups have undecidable word problem even when S, T, U satisfy nice conditions. Here we consider amalgams of inverse semigroups where S and T have decidable word problem, U has decidable membership problem and we give some sufficient conditions for the associated amalgamated free product having decidable word problem.

On the decidability of the word problem for amalgamated free products of inverse semigroups.

CHERUBINI, ALESSANDRA
2008-01-01

Abstract

A triple [S,T;U] where S and T are inverse semigroups and U is the intersection of S and T is called an amalgam of inverse semigroups. The amalgamated free product associated to the amalgam [S,T;U] is defined by the usual universal diagram and it is well-known that each amalgams of inverse semigroups embeds in its associated aalgamated free product. In general amalgamated free products of inverse semigroups have undecidable word problem even when S, T, U satisfy nice conditions. Here we consider amalgams of inverse semigroups where S and T have decidable word problem, U has decidable membership problem and we give some sufficient conditions for the associated amalgamated free product having decidable word problem.
2008
Inverse semigroups - Presentation - Amalgamated free products - Schützenberger automata
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/546328
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