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The word problem for one-relator semigroups

  • James Howie (a1) and Stephen J. Pride (a1)
Extract

Diagrams have been used in group theory by numerous authors, and have led to significant results (see [4] and the references cited there). The idea of applying diagrams to semigroups seems to be more recent [3, 7, 8]. In the present paper we discuss semi group diagrams and use them to obtain results concerning the word problem for one-relator semigroups. The word problem for one-relator groups has been solved by Magnus [6], but the analogous question for semigroups remains open. We are not able to solve the problem in full generality, but have obtained some partial results.

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COPYRIGHT: © Cambridge Philosophical Society 1986
References
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[12]Adyan, S. I. and Oganesyan, G. U.. On the word and divisibility problems in semigroups with a single defining relation. Izv. Akad. Nauk SSSR Ser. Mat. 43 (1978), 219–225; Math. USSR Izv. 12 (1978), 207–212.
[13]Book, R. V. and Squier, C.. Almost all one-rule Thue systems have decidable word problems. Discrete Math. 49 (1984), 237–240.
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[15]Lallement, G.. On monoids presented by a single relation. J. Algebra 32 (1974), 370–388.
[16]Oganesyan, G. U.. On the problems of equality and divisibility of words in a semigroup with a defining relation of the form a = bA. Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), 602–612
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[17]Oganesyan, G. U.. On semigroups with a single relation and semigroups without cycles. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 88–94
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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