Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 42-44
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N. E. Shavgulidze. Special classes of $l$-rings and Anderson–Divinsky–Sulinski lemma. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 42-44. http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a7/
@article{VMUMM_2010_2_a7,
author = {N. E. Shavgulidze},
title = {Special classes of $l$-rings and {Anderson{\textendash}Divinsky{\textendash}Sulinski} lemma},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {42--44},
year = {2010},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a7/}
}
TY - JOUR
AU - N. E. Shavgulidze
TI - Special classes of $l$-rings and Anderson–Divinsky–Sulinski lemma
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 2010
SP - 42
EP - 44
IS - 2
UR - http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a7/
LA - ru
ID - VMUMM_2010_2_a7
ER -
%0 Journal Article
%A N. E. Shavgulidze
%T Special classes of $l$-rings and Anderson–Divinsky–Sulinski lemma
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2010
%P 42-44
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a7/
%G ru
%F VMUMM_2010_2_a7
If $\rho$ is a radical in the class of rings and $I$ is an ideal of a ring $R$, then $\rho(I)$ is an ideal of $R$ (the Anderson–Divinsky–Sulinski lemma). Let $\rho$ be a special radical in the class of $l$-rings (lattice-ordered rings) and $I$ be an $l$-ideal of an $l$-ring $R$. In this paper we prove that $\rho(I)$ is an $l$-ideal of the $l$-ring $R$ and $\rho(I)=\rho(R)\cap I$.
