Geodesic
Radicals of $l$-rings and one-sided $l$-ideals
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 169-181
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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. 
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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/

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