Geodesic
Special classes of $l$-rings and Anderson--Divinsky--Sulinski lemma
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 42-44

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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 $\rho(I)=\rho(R)\cap I$. 
@article{VMUMM_2010_2_a7,
     author = {N. E. Shavgulidze},
     title = {Special classes of $l$-rings and {Anderson--Divinsky--Sulinski} lemma},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {42--44},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a7/}
}
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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/