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 | References | Similar Articles | Additional Information
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 $\max \;(\operatorname {length} B,\operatorname {length} C)$.
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. MR 0207802
- Ju. V. Matijasevič, Simple examples of unsolvable associative calculi, Dokl. Akad. Nauk SSSR 173 (1967), 1264–1266 (Russian). MR 0216955
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Additional Information
Keywords:
Semigroup,
one defining relation,
generator,
word problem,
solvable
Article copyright:
© Copyright 1970
American Mathematical Society