Skip to main content

Some algorithms for semigroups and monoids presented by a single relation

Part of the Lecture Notes in Mathematics book series (LNM,volume 1320)

Keywords

  • Word Problem
  • Primary Word
  • Semi Group
  • Single Relation
  • Cancellative Semigroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • S. I. Adjan, 1966, Defining relations and algorithmic problems for groups and semigroups, Tr. Mat. Inst. Steklov, 85, 1–124 (Russian), Am. Math. Soc. Transl., 152, 1967.

    MathSciNet  Google Scholar 

  • S. I. Adjan, 1977, On word transformations in semigroups given by systems of defining relations, Algebra i Logika, 15, no. 6, 611–621 (Russian).

    MathSciNet  Google Scholar 

  • S. I. Adjan, G. U. Oganesjan, 1978, On the problems of equality and divisibility in semigroups with one defining relation, Izv. Akad. Nauk SSSR, Ser. Mat., 42, no. 2, 219–225 (Russian).

    MathSciNet  Google Scholar 

  • James Howie, S. J. Pride, 1986, The word problem for one-relator semigroups, Math. Proc. Cambridge Phil. Soc. 99, 33–44.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • D. A. Jackson, 1986, Some one-relator semigroup presentations with solvable word problems, Math. Proc. Cambridge Phil. Soc., 99, 433–434.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • G. Lallement, 1974, On monoids presented by a single relation. J. of Algebra, 32, 370–388.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • W. Magnus, 1932, Das Identitäts-Problem für Gruppen mit einer definierenden Relation, Math. Ann. 106, 295–307.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • A. A. Markov, 1947, On the impossibility of certain algorithms in the theory of associative systems, Dokl. Akad. Nauk. 55, 587–590 and 58, 353–356 (Russian).

    MathSciNet  Google Scholar 

  • J. Matyasevitch, 1967, Simple examples of unsolvable associative calculi, Dokl. Akad. Nauk, 173, 1264–1266; Tr. Mat. Inst. Steklov, 93, 50–88 (Russian).

    MathSciNet  Google Scholar 

  • G. U. Oganesjan, 1978, On the problems of equality and divisibility in semigroups with defining relations of the form a = bA, Izv. Akad. Nauk SSSR, Ser. Mat., 42, no. 3, 602–612 (Russian).

    MathSciNet  Google Scholar 

  • G. U. Oganesjan, 1982, On semigroups with one relation and semigroups without cycles, Izv. Akad. Nauk SSSR, Ser. Mat., 46, no. 1, 88–94 (Russian).

    MathSciNet  Google Scholar 

  • E. J. Post, 1947, Recursive unsolvability of a problem of Thue, J. of Symb. Logic, 12, 1–11.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • J. H. Remmers, 1980, On the geometry of semigroup presentations, Adv. in Math., 36, 283–296.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • O. A. Sarkisjan, 1981, On the problems of equality and divisibility in semigroups and groups without cycles, Izv. Akad. Nauk SSSR, Ser. Mat. 45, no. 6, 1424–1441 (Russian).

    MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Lallement, G. (1988). Some algorithms for semigroups and monoids presented by a single relation. In: Jürgensen, H., Lallement, G., Weinert, H.J. (eds) Semigroups Theory and Applications. Lecture Notes in Mathematics, vol 1320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083431

Download citation

  • DOI: https://doi.org/10.1007/BFb0083431

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19347-0

  • Online ISBN: 978-3-540-39225-5

  • eBook Packages: Springer Book Archive