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

Abstract : We study inverse semigroup amalgams [S 1 , S 2 ; U ], where S 1 and S 2 are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S 1 and S 2. We use a modified version of Bennett's work on the structure of Schützenberger graphs of the R-classes of S 1 * U S 2 to state sufficient conditions for the amalgamated free products S 1 * U S 2 having decidable word problem.
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Marco Mazzucchelli, Alessandra Cherubini. On the decidability of the word problem for amalgamated free products of inverse semigroups. Semigroup Forum, Springer Verlag, 2008, 76, pp.309 - 329. ⟨10.1007/s00233-007-9030-8⟩. ⟨ensl-01404257⟩

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