Geodesic
On the problems of equality and divisibility of words in a~semigroup with a~defining relation of the from
Izvestiya. Mathematics , Tome 12 (1978) no. 3, pp. 557-566

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This paper studies the problem of left divisibility in a semigroup given by a single defining relation of the form $a=bA$, where $A$ is an arbitrary word in the alphabet $a,b$. Solvability of the problems of equality and left divisibility of words is proved for a semigroup given by a defining relation of the form $a=(bA)^na$, where $n>1$ . Bibliography: 4 titles. 
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     author = {G. U. Oganesyan},
     title = {On the problems of equality and divisibility of words in a~semigroup with a~defining relation of the from},
     journal = {Izvestiya. Mathematics },
     pages = {557--566},
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     volume = {12},
     number = {3},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_3_a7/}
}
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G. U. Oganesyan. On the problems of equality and divisibility of words in a~semigroup with a~defining relation of the from. Izvestiya. Mathematics , Tome 12 (1978) no. 3, pp. 557-566. http://geodesic.mathdoc.fr/item/IM2_1978_12_3_a7/