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Algorithmic Problems for Amalgams of Finite Semigroups

✍ Scribed by Mark V. Sapir

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
118 KB
Volume
229
Category
Article
ISSN
0021-8693

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✦ Synopsis

We prove that there exists an amalgam of two finite 4-nilpotent semigroups such that the corresponding amalgamated product has an undecidable word problem. We also show that the problem of embeddability of finite semigroup amalgams in any semigroups and the problem of embeddability of finite semigroup amalgams into finite semigroups are undecidable. We use several versions of Minsky algorithms and Slobodskoj's result about undecidability of the universal theory of finite groups.

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U have the same set of idempotents , then the amalgam is strongly embeddable in a regular semigroup S that contains S , S , and U as full regular subsemigroups. In 1 2 this case the inductive structure of the amalgamated free produce S ) S was 1 U 2 studied by Nambooripad and Pastijn in 1989, using