Geodesic
Special classes of $l$-rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 157-173

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We study a special class of lattice-ordered rings and a special radical. We prove that a special radical of an $l$-ring is equal to the intersection of the right $l$-prime $l$-ideals for each of which the following condition holds: the quotient $l$-ring by the maximal $l$-ideal contained in a given right $l$-ideal belongs to the special class. The prime radical of an $l$-ring is equal to the intersection of the right $l$-semiprime $l$-ideals. We introduce the notion of a completely $l$-prime $l$-ideal. We prove that $N_3(R)$ is equal to the intersection of the completely $l$-prime, right $l$-ideals of an $l$-ring $R$, where $N_3(R)$ is the special radical of the $l$-ring $R$ defined by the class of $l$-rings without positive divisors of zero. 
@article{FPM_2009_15_1_a11,
     author = {N. E. Shavgulidze},
     title = {Special classes of $l$-rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {157--173},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a11/}
}
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N. E. Shavgulidze. Special classes of $l$-rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 157-173. http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a11/