We study inverse semigroup amalgams of the form of free inverse semigroups S,T with core an arbitrary finitely generated inverse subsemigroup of S and T. We show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where the word problem for a semigroup amalgam is in general undecidable, even if S and T have decidable word problem, U is a free semigroup, and the membership problem for U in S and T is decidable. We also obtain a number of results concerning the structure of such amalgams.

Amalgams of free inverse semigroups

CHERUBINI, ALESSANDRA;
1997-01-01

Abstract

We study inverse semigroup amalgams of the form of free inverse semigroups S,T with core an arbitrary finitely generated inverse subsemigroup of S and T. We show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where the word problem for a semigroup amalgam is in general undecidable, even if S and T have decidable word problem, U is a free semigroup, and the membership problem for U in S and T is decidable. We also obtain a number of results concerning the structure of such amalgams.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/519644
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