Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 91-96
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E. S. Golod. On noncommutative Gröbner 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/
@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},
year = {2004},
volume = {10},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a6/}
}
TY - JOUR
AU - E. S. Golod
TI - On noncommutative Gröbner bases over rings
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2004
SP - 91
EP - 96
VL - 10
IS - 4
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 Gröbner bases over rings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2004
%P 91-96
%V 10
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a6/
%G ru
%F FPM_2004_10_4_a6
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.
