Geodesic
Radicals and $l$-modules
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 235-243.

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We show that for any special class of $l$-modules, we can define a special class of $l$-rings. We prove that the special radical of an $l$-ring $R$ can be represented as the intersection of the $l$-annihilators of $l$-modules over $R$ belonging to the special class. The prime radical of an $l$-ring $R$ can be represented as the intersection of the $l$-annihilators of $l$-prime $l$-modules over $R$. 
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N. E. Shavgulidze. Radicals and $l$-modules. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 235-243. http://geodesic.mathdoc.fr/item/FPM_2009_15_7_a12/

[1] Andrunakievich V. A., Ryabukhin Yu. M., “Spetsialnye moduli i spetsialnye radikaly”, DAN SSSR, 147 (1962), 1274–1277 | Zbl

[2] Birkgof G., Teoriya reshëtok, Mir, M., 1984 | MR

[3] Mikhalëv A. V., Shatalova M. A., “Pervichnyi radikal reshëtochno uporyadochennykh kolets”, Sb. rabot po algebre, Izd-vo Mosk. un-ta, M., 1989, 178–184

[4] Fuks L., Uporyadochennye algebraicheskie sistemy, Nauka, M., 1965 | Zbl

[5] Shavgulidze N. E., “Radikaly $l$-kolets i odnostoronnie $l$-idealy”, Fundament. i prikl. mat., 14:8 (2008), 169–181 | MR

[6] Shavgulidze N. E., “Spetsialnye klassy $l$-kolets”, Fundament. i prikl. mat., 15:1 (2009), 157–173

[7] Shavgulidze N. E., “Spetsialnye klassy $l$-kolets i lemma Andersona–Divinskogo–Sulinskogo”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2010, no. 2, 42–44 | MR

[8] Shavgulidze N. E., “Radikaly $l$-kolets i spetsialnye klassy $l$-modulei”, Uspekhi mat. nauk (to appear)

[9] Shatalova M. A., “$l_A$- i $l_I$-koltsa”, Sib. mat. zhurn., 7:6 (1966), 1383–1389

[10] Shatalova M. A., “K teorii radikalov v strukturno uporyadochennykh koltsakh”, Mat. zametki, 4:6 (1968), 639–648 | MR | Zbl