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

Marco Mazzucchelli (1) , Alessandra Cherubini (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 POLIMI - Politecnico di Milano [Milan]

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.

Keywords: inverse semigroups; presentation; amalgamated free products; Schützenberger automata

Domains: Mathematics [math]

Marco Mazzucchelli, Alessandra Cherubini. On the decidability of the word problem for amalgamated free products of inverse semigroups. Semigroup Forum, 2008, 76, pp.309 - 329. ⟨10.1007/s00233-007-9030-8⟩. ⟨ensl-01404257⟩