Geodesic
Gr\"obner bases and coherentness of monomial associative algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 2, pp. 501-509.

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. 
@article{FPM_1996_2_2_a6,
     author = {D. I. Piontkovskii},
     title = {Gr\"obner bases and coherentness of monomial associative algebras},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {501--509},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a6/}
}
TY  - JOUR
AU  - D. I. Piontkovskii
TI  - Gr\"obner bases and coherentness of monomial associative algebras
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1996
SP  - 501
EP  - 509
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a6/
LA  - ru
ID  - FPM_1996_2_2_a6
ER  - 
%0 Journal Article
%A D. I. Piontkovskii
%T Gr\"obner bases and coherentness of monomial associative algebras
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1996
%P 501-509
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a6/
%G ru
%F FPM_1996_2_2_a6
D. I. Piontkovskii. Gr\"obner 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/