Geodesic
Gröbner bases and coherentness of monomial associative algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 2, pp. 501-509 
D. I. Piontkovskii. Gröbner bases and coherentness of monomial associative algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 2, pp. 501-509. http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a6/
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     author = {D. I. Piontkovskii},
     title = {Gr\"obner bases and coherentness of monomial associative algebras},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {501--509},
     year = {1996},
     volume = {2},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $A$ be an associative algebra which is defined by a finite number of monomial relations. In this paper we show that any finitely generated one-sided ideal in $A$ has a finite Gröbner basis. We propose an algorithm for constructing of this basis. As a consequence we obtain an algorithm for computation of syzygy module for the system of generators of the ideal. In particular, this syzygy module is finitely generated. It means that $A$ is coherent.