Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T06:51:52.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Free bands and free *-bands

Published online by Cambridge University Press:  18 May 2009

J. A. Gerhard  and
Mario Petrich
J. A. Gerhard
Affiliation:
University Of Manitoba, Winnipeg, Canada
Mario Petrich
Affiliation:
University Of Manitoba, Winnipeg, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The word problem for free bands (idempotent semigroups) was solved by Green and Rees [4] in an early paper. They also established certain properties of the free band. This was followed by McLean [6] who provided a general structure theory for bands with some indication as to the structure of the free band. Since then a great many papers have appeared dealing with various aspects of the topic of bands and their varieties. A different solution of the word problem for free bands was recently given by Siekmann and Szabó [9]. For a discussion of bands, see the books [5] and [8].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 161 - 179
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

1.Adair, C. L., Bands with involution, J. Algebra 75 (1982), 297–314.CrossRefGoogle Scholar
2.Gerhard, J. A. and Petrich, M., The word problem for orthogroups, Canad. J. Math. 33 (1981), 893–900.CrossRefGoogle Scholar
3.Gerhard, J. A. and Petrich, M., Free involutorial completely simple semigroups, Canad. J. Math. 37 (1985), 271–295.CrossRefGoogle Scholar
4.Green, J. A. and Rees, D., On semi-groups in which xr = x, Proc. Cambridge Phil. Soc. 48 (1952), 35–40.CrossRefGoogle Scholar
5.Howie, J. M., An introduction to semigroup theory, (Academic Press, 1976).Google Scholar
6.McLean, D., Idempotent semigroups, Amer. Math. Monthly 61 (1954), 110–113.CrossRefGoogle Scholar
7.Nordahl, T. E. and Scheiblich, H. E., Regular *-semigroups, Semigroup Forum 16 (1978), 369–377.CrossRefGoogle Scholar
8.Petrich, M., Lectures in semigroups, (Akademie-Verlag, 1977).CrossRefGoogle Scholar
9.Siekmann, J. and Szabó, P., A noetherian and confluent rewrite system for idempotent semigroups, Semigroup Forum 25 (1982), 83–110.CrossRefGoogle Scholar
10.Yamada, M., Finitely generated free *-bands, Semigroup Forum 29 (1984), 13–16.CrossRefGoogle Scholar