Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 169-181
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N. E. Shavgulidze. Radicals of $l$-rings and one-sided $l$-ideals. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 169-181. http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a10/
@article{FPM_2008_14_8_a10,
author = {N. E. Shavgulidze},
title = {Radicals of $l$-rings and one-sided $l$-ideals},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {169--181},
year = {2008},
volume = {14},
number = {8},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a10/}
}
TY - JOUR
AU - N. E. Shavgulidze
TI - Radicals of $l$-rings and one-sided $l$-ideals
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2008
SP - 169
EP - 181
VL - 14
IS - 8
UR - http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a10/
LA - ru
ID - FPM_2008_14_8_a10
ER -
%0 Journal Article
%A N. E. Shavgulidze
%T Radicals of $l$-rings and one-sided $l$-ideals
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 169-181
%V 14
%N 8
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a10/
%G ru
%F FPM_2008_14_8_a10
In this paper, we introduce the notion of an $l$-prime $l$-ideal and that of a right $l$-semiprime $l$-ideal. We prove that our definitions coincide with the definitions of M. A. Shatalova in the case of two-sided $l$-ideals. Our main results are the following ones. The radical of an $l$-ring can be represented as the intersection of the right $l$-ideals for each of which the following condition holds: the quotient ring by the maximal $l$-ideal contained in the given right $l$-ideal is semisimple. The hypernilpotent radical of an $l$-ring can be represented as the intersection of the right $l$-semiprime ideals satisfying the same condition.
