Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T01:01:51.317Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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