Geodesic
On the word and divisibility problems in semigroups with a~single defining relation
Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 207-212

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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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     author = {S. I. Adian and G. U. Oganesyan},
     title = {On the word and divisibility problems in semigroups with a~single defining relation},
     journal = {Izvestiya. Mathematics },
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     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a0/}
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S. I. Adian; G. U. Oganesyan. On the word and divisibility problems in semigroups with a~single defining relation. Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 207-212. http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a0/