Geodesic
On noncommutative Gr\"obner bases over rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 91-96.

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

Let $R$ be a commutative ring. It is proved that for verification whether a set of elements $\{f_\alpha\}$ of the free associative algebra over $R$ is a Gröbner basis (with respect to some admissible monomial order) of the (bilateral) ideal that the elements $f_\alpha $ generate it is sufficient to check reducibility to zero of $S$-polynomials with respect to $\{f_\alpha\}$ iff $R$ is an arithmetical ring. Some related open questions and examples are also discussed. 
@article{FPM_2004_10_4_a6,
     author = {E. S. Golod},
     title = {On noncommutative {Gr\"obner} bases over rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {91--96},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a6/}
}
TY  - JOUR
AU  - E. S. Golod
TI  - On noncommutative Gr\"obner bases over rings
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2004
SP  - 91
EP  - 96
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a6/
LA  - ru
ID  - FPM_2004_10_4_a6
ER  - 
%0 Journal Article
%A E. S. Golod
%T On noncommutative Gr\"obner bases over rings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2004
%P 91-96
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a6/
%G ru
%F FPM_2004_10_4_a6
E. S. Golod. On noncommutative Gr\"obner bases over rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 91-96. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a6/

[1] Golod E. S., “Arifmeticheskie koltsa, biendomorfizmy i bazisy Grëbnera”, Uspekhi mat. nauk, 60:1 (2005), 167–168 | MR | Zbl

[2] Golod E. S., “Standard bases and homology”, Lect. Notes Math., 1352, 1988, 105–110 | MR