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

This article is cited in 7 scientific papers (total in 8 papers)

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.

Full text: PDF file (716 kB)
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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
Received: 14.02.1977

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  mathscinet  zmath
    2. G. U. Oganesyan, “On semigroups with one relation and semigroups without cycles”, Math. USSR-Izv., 20:1 (1983), 89–95  mathnet  crossref  mathscinet  zmath
    3. S. I. Adian, “On the divisibility problem for one-relator monoids”, Math. Notes, 55:1 (1994), 3–7  mathnet  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Yu. E. Trubitsyn, “Semigroups presented by one relation and satisfying the Church–Rosser property”, Math. Notes, 61:1 (1997), 96–99  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Kayoko Shikishima-Tsuji, Masashi Katsura, Yuji Kobayashi, “On termination of confluent one-rule string-rewriting systems”, Information Processing Letters, 61:2 (1997), 91  crossref
    7. S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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