Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 151-163
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A. Mekei. On the representation of finite rings by matrices over commutative rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 151-163. http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a7/
@article{FPM_2012_17_7_a7,
author = {A. Mekei},
title = {On the representation of finite rings by matrices over commutative rings},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {151--163},
year = {2012},
volume = {17},
number = {7},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a7/}
}
TY - JOUR
AU - A. Mekei
TI - On the representation of finite rings by matrices over commutative rings
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2012
SP - 151
EP - 163
VL - 17
IS - 7
UR - http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a7/
LA - ru
ID - FPM_2012_17_7_a7
ER -
%0 Journal Article
%A A. Mekei
%T On the representation of finite rings by matrices over commutative rings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2012
%P 151-163
%V 17
%N 7
%U http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a7/
%G ru
%F FPM_2012_17_7_a7
In this paper, it is shown that all finite associative rings satisfying the identities $nx=0$ and $x^3f(x)+x^2=0$, where $n$ is an odd natural number and $f(x)\in\mathbb Z[x]$, are embeddable in the ring of matrices over some suitable commutative ring.
[2] Mekei A., O mnogoobraziyakh, porozhdënnykh konechnymi assotsiativnymi koltsami, i svoistvakh ekstremalnosti i kritichnosti, Dis. $\dots$ dokt. fiz.-mat. nauk, M., 1995
[3] Nechaev A. A., “Konechnye koltsa glavnykh idealov”, Mat. sb., 91(133):3(7) (1973), 350–366 | MR | Zbl
[4] Bergman G. M., Britten D. J., Lemire F. W., “Embedding rings in completed graded rings. III. Algebras over general $k$”, J. Algebra, 84:1 (1983), 42–61 | DOI | MR | Zbl