Geodesic
On semigroups with one relation and semigroups without cycles
Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 89-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1983_20_1_a4,
     author = {G. U. Oganesyan},
     title = {On semigroups with one relation and semigroups without cycles},
     journal = {Izvestiya. Mathematics },
     pages = {89--95},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a4/}
}
TY  - JOUR
AU  - G. U. Oganesyan
TI  - On semigroups with one relation and semigroups without cycles
JO  - Izvestiya. Mathematics 
PY  - 1983
SP  - 89
EP  - 95
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a4/
LA  - en
ID  - IM2_1983_20_1_a4
ER  - 
%0 Journal Article
%A G. U. Oganesyan
%T On semigroups with one relation and semigroups without cycles
%J Izvestiya. Mathematics 
%D 1983
%P 89-95
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a4/
%G en
%F IM2_1983_20_1_a4
G. U. Oganesyan. On semigroups with one relation and semigroups without cycles. Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 89-95. http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a4/

[1] Adyan S. I., Opredelyayuschie sootnosheniya i algoritmicheskie problemy dlya grupp i polugrupp, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 85, 1966 | Zbl

[2] Adyan S. I., “O preobrazovaniyakh slov v polugruppe, zadannoi sistemoi opredelyayuschikh sootnoshenii”, Algebra i logika, 15:6 (1976), 611–621 | MR | Zbl

[3] Adyan S. I., Oganesyan G. U., “K problemam ravenstva i delimosti v polugruppakh s odnim opredelyayuschim sootnosheniem”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 219–225 | MR | Zbl

[4] Sarkisyan O. A., “O problemakh tozhdestva i delimosti v polugruppakh i gruppakh bez tsiklov”, Izv. AN SSSR. Ser. matem., 45:6 (1981), 1424–1441 | MR

[5] Oganesyan G. U., “O problemakh ravenstva i delimosti v polugruppe s opredelyayuschim sootnosheniem vida $a=bA$”, Izv. AN SSSR. Ser. matem., 42:3 (1978), 602–612 | MR | Zbl