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 Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 2, Pages 219–225 (Mi izv1710)

On the word and divisibility problems in semigroups with a single defining relation

S. I. Adian, G. U. Oganesyan

Abstract: It is proved that the word problem and left (right) divisibility problem in an arbitrary semigroup with a single defining relation can be reduced to the respective problems for a single relation which is left (or right) noncancellative.
Bibliography: 2 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1978, 12:2, 207–212

Bibliographic databases:

Document Type: Article
UDC: 519.444
MSC: Primary 20M05; Secondary 20F47

Citation: S. I. Adian, G. U. Oganesyan, “On the word and divisibility problems in semigroups with a single defining relation”, Izv. Akad. Nauk SSSR Ser. Mat., 42:2 (1978), 219–225; Math. USSR-Izv., 12:2 (1978), 207–212

Citation in format AMSBIB
\Bibitem{AdiHov78} \by S.~I.~Adian, G.~U.~Oganesyan \paper On the word and divisibility problems in semigroups with a~single defining relation \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1978 \vol 42 \issue 2 \pages 219--225 \mathnet{http://mi.mathnet.ru/izv1710} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=480782} \zmath{https://zbmath.org/?q=an:0389.20047|0401.20050} \transl \jour Math. USSR-Izv. \yr 1978 \vol 12 \issue 2 \pages 207--212 \crossref{https://doi.org/10.1070/IM1978v012n02ABEH001848} 

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This publication is cited in the following articles:
1. G. U. Oganesyan, “On the problems of equality and divisibility of words in a semigroup with a defining relation of the from”, Math. USSR-Izv., 12:3 (1978), 557–566
2. G. U. Oganesyan, “On semigroups with one relation and semigroups without cycles”, Math. USSR-Izv., 20:1 (1983), 89–95
3. S. I. Adian, “On the divisibility problem for one-relator monoids”, Math. Notes, 55:1 (1994), 3–7
4. V. S. Guba, “On the relationship between the problems of equality and divisibility of words for semigroups with a single defining relation”, Izv. Math., 61:6 (1997), 1137–1169
5. Yu. E. Trubitsyn, “Semigroups presented by one relation and satisfying the Church–Rosser property”, Math. Notes, 61:1 (1997), 96–99
6. Kayoko Shikishima-Tsuji, Masashi Katsura, Yuji Kobayashi, “On termination of confluent one-rule string-rewriting systems”, Information Processing Letters, 61:2 (1997), 91
7. S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296
8. L. D. Beklemishev, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, M. R. Pentus, A. A. Razborov, A. L. Semenov, V. A. Uspenskii, “Sergei Ivanovich Adian (on his 75th birthday)”, Russian Math. Surveys, 61:3 (2006), 575–588
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