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Abstract
Abstract For any hereditary Kurosh-Amitsur radical r of right Lie algebras the factor algebras L/r(L) for all L, are either Lie algebras, or proper right Lie algebras with some additional property (Theorem 1). A radical r is an ADS-radical if and only if r is strongly characteristic (Theorem 2). For any hereditary radical ru of Lie algebras its unique hereditary extension ru to right Lie algebras is given in Theorems 3 and 4. An extension ru of a radical rv of Lie algebras to right Lie algebras, is an ADS-radical if and only if so is rv (Theorem 5).
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