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 Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 88–94 (Mi izv1606)

On semigroups with one relation and semigroups without cycles

G. U. Oganesyan

Abstract: The left divisibility problem for semigroups without left cycles is reduced to the same problem for semigroups which describe certain transformations of words in the original semigroup. Using this reduction one can solve positively the word and left divisibility problems for semigroups of the form $\langle a,b; a=bAa\rangle$, where $A$ is an arbitrary word in the alphabet $a,b$.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 89–95

Bibliographic databases:

UDC: 519.444
MSC: Primary 20M05; Secondary 03D40

Citation: G. U. Oganesyan, “On semigroups with one relation and semigroups without cycles”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 88–94; Math. USSR-Izv., 20:1 (1983), 89–95

Citation in format AMSBIB
\Bibitem{Hov82} \by G.~U.~Oganesyan \paper On semigroups with one relation and semigroups without cycles \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1982 \vol 46 \issue 1 \pages 88--94 \mathnet{http://mi.mathnet.ru/izv1606} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=643894} \zmath{https://zbmath.org/?q=an:0506.20024|0492.20039} \transl \jour Math. USSR-Izv. \yr 1983 \vol 20 \issue 1 \pages 89--95 \crossref{https://doi.org/10.1070/IM1983v020n01ABEH001340} 

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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. David A. Jackson, “Some one-relator semigroup presentations with solvable word problems”, Math Proc Camb Phil Soc, 99:3 (1986), 433
2. James Howie, Stephen J. Pride, “The word problem for one-relator semigroups”, Math Proc Camb Phil Soc, 99:1 (1986), 33
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. Yuji Kobayashi, “Homotopy reduction systems for monoid presentations Asphericity and low-dimensional homology”, Journal of Pure and Applied Algebra, 130:2 (1998), 159
6. S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296
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