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Some one-relator semigroup presentations with solvable word problems

Published online by Cambridge University Press:  24 October 2008

David A. Jackson
David A. Jackson
Affiliation:
Parks College of St Louis University, Cahokia, IL 62206, U.S.A.
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Extract

We provide, for N ≥ 1, a solution to the word problem for the semigroup S having the presentation {a, b|a = abaNb}. For N = 2, this is example 7 in Howie and Pride [1]. Since solving the word problem for {a, b|a = abaNb} is equivalent to solving the word problem for {a, b|a = baNba}, the result here should be regarded as a special case of a more general result of Oganesyan [2], who solves the word problem for {a, b|a = bA}, A arbitrary.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 433 - 434
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Howie, J. and Pride, S. J.. The word problem for one-relator semigroups. Math. Proc. Cambridge Philos. Soc. 99 (1986), 33–44.CrossRefGoogle Scholar
[2]Oganesyan, G. U.. On semigroups with one relation and semigroups without cycles. Math. USSR Izvestiya 20 (1983), 89–95.CrossRefGoogle Scholar