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The solvability of the word problem for certain semigroups


Author: Ann Yasuhara
Journal: Proc. Amer. Math. Soc. 26 (1970), 645-650
MSC: Primary 20.10
DOI: https://doi.org/10.1090/S0002-9939-1970-0268257-9
MathSciNet review: 0268257
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Abstract: This paper establishes the solvability of the word problem for semigroups with one defining relation if that relation is of the form $ A \sim BtC$ where (1) $ A$ and $ BtC$ are words on the generators of the semigroup but the generator $ t$ does not occur in $ A,B$ or $ C$ and (2) the length of $ A$ is greater than the $ \max \;(\operatorname{length} B,\operatorname{length} C)$.


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  • [1] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617. MR 0207802 (34:7617)
  • [2] Ju. V. Matijasevič, Simple examples of undecidable associative calculi, Dokl. Akad. Nauk SSSR 173 (1967), 1264-1266 = Soviet Math. Dokl. 8 (1967), 555-557. MR 0216955 (36:50)

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DOI: https://doi.org/10.1090/S0002-9939-1970-0268257-9
Keywords: Semigroup, one defining relation, generator, word problem, solvable
Article copyright: © Copyright 1970 American Mathematical Society

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