Inverse semigroup amalgams with a lower bounded core

Paul Bennett

Abstract


We consider inverse semigroup amalgams [S1,S2;U] such that for any u ∈ U and e ∈ E(Si) with u ≥ e in Si, where i ∈ {1,2}, there exists f ∈ E(U) with u ≥ f ≥ e in Si; we say that U is lower bounded in S1 and S2. We construct and describe the Schutzenberger automata of S1∗U S2 and give conditions for decidable word problem. The homomorphisms of the Schutzenberger graphs of S1∗U S2 are studied and conditions are given for S1∗U S2 to be completely semisimple. In the case when S1 and S2 have decidable word problems and U is finite, we show that S1∗U S2 has decidable word problem.

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Published: 2020-01-07

How to Cite this Article:

Paul Bennett, Inverse semigroup amalgams with a lower bounded core, J. Semigroup Theory Appl., 2020 (2020), Article ID 3

Copyright © 2020 Paul Bennett. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

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