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Prime radicals of \(\mathcal{K}\)-ordered algebras as Kurosh radicals. (Russian. English summary) Zbl 1431.06009
Summary: The Kopytov’s order for any algebras over a field is considered. Some results concerned with the properties of a factor algebra for a lattice of \(\mathcal{K}\)-ordered algebras and its \(l\)-prime radical are obtained. Also, some results concerned with the properties of ordered homomorphisms, strictly ordered homomorphisms and lattice homomorphisms of lattice ordered algebras are presented.
MSC:
06F25 Ordered rings, algebras, modules
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References:
[1] Andrunakievich V. A., Ryabukhin Yu. M., Radikaly algebr i strukturnaya teoriya, Nauka, M., 1979, 496 pp.
[2] Kopytov V. M., “Reshetochno uporyadochennye algebry Li”, Sib. mat. zhurn., XVIII:3 (1977), 595-607 · Zbl 0365.06010
[3] Kopytov V. M., Reshetochno uporyadochennye gruppy, Nauka, M., 1984, 320 pp. · Zbl 0567.06011
[4] Kopytov V. M., “Uporyadochenie algebr Li”, Algebra i logika, 11:3 (1972), 295-325 · Zbl 0253.17006
[5] Kochetova Yu. V., “Pervichnye i polupervichnye reshetochno uporyadochennye algebry Li”, Fundamentalnaya i prikladnaya matematika, 14:7 (2008), 137-143
[6] Kochetova Yu. V., “Pervichnyi radikal reshetochno uporyadochennykh algebr Li”, Uspekhi matematicheskikh nauk, 63:5 (2008), 191-192 · Zbl 1184.06009
[7] Kochetova Yu. V., “O \(l\)-pervichnom radikale reshetochno uporyadochennykh algebr”, Fundamentalnaya i prikladnaya matematika, 17:5 (2011-2012), 55-68 · Zbl 1271.70021
[8] Kochetova Yu. V., Shirshova E. E., “O gomomorfizmakh chastichno uporyadochennykh algebr Li”, Izbrannye voprosy algebry: sbornik statei, posvyaschennyi pamyati N. Ya. Medvedeva, Izd-vo Alt. un-ta, Barnaul, 2007, 131-142
[9] Kochetova Yu. V., Shirshova E. E., “O lineino uporyadochennykh lineinykh algebrakh”, Fundamentalnaya i prikladnaya matematika, 15:1 (2009), 53-63 · Zbl 1228.11007
[10] Kurosh A. G., “Radikaly kolets i algebr”, Mat. sb., 33:1 (1953), 13-26 · Zbl 0050.26101
[11] Lambek I., Koltsa i moduli, Mir, M., 1971 · Zbl 0229.16001
[12] Mikhalëv A. V., Shatalova M. A., “Pervichnyi radikal reshetochno uporyadochennykh grupp”, Vestnik Mosk. un-ta. Ser. Matematika. Mekhanika, 1990, no. 2, 84-86
[13] Mikhalëv A. V., Shatalova M. A., “Pervichnyi radikal reshetochno uporyadochennykh kolets”, Sb. rabot po algebre, Izd-vo Mosk. un-ta, M., 1989, 178-184
[14] Mikhalëv A. V., Shirshova E. E., “Pervichnyi radikal \(pl\)-grupp”, Fundamentalnaya i prikladnaya matematika, 12:2 (2006), 193-199
[15] Pikhtilkov S. A., Strukturnaya teoriya spetsialnykh algebr Li, Izd-vo Tul. gos. ped. un-ta im. L. N. Tolstogo, Tula, 2005, 130 pp.
[16] Fuks L., Chastichno uporyadochennye algebraicheskie sistemy, Mir, M., 1965
[17] Schukin K. K., “\(RI\)-razreshimyi radikal gruppy”, Mat. sb., 52:4 (1960), 1021-1031 · Zbl 0107.02002
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