Abstract
We consider HNN extensions where U 1 and U 2 are inverse monoids of an inverse semigroup S such that, for any and with in S, there exists with in S, for we say that U 1 and U 2 are lower bounded in S. We construct and describe the Schützenberger automata of and give conditions for to have decidable word problem. Homomorphisms of the Schützenberger graphs of are studied and conditions are given for to be completely semisimple. When S has decidable word problem and U 1 and U 2 are finite, we show that has decidable word problem. The class of HNN extensions considered here is surprisingly useful and generalizes the class introduced by Jajcayová. A future paper intends to show that any HNN extension of an inverse semigroup can be embedded into an HNN extension where the subsemigroups are lower bounded.
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