ON KUROSH—AMITSUR RADICALS OF RIGHT LIE ALGEBRAS

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 r_u of Lie algebras its unique hereditary extension r_u to right Lie algebras is given in Theorems 3 and 4. An extension r_u of a radical r_v of Lie algebras to right Lie algebras, is an ADS-radical if and only if so is r_v (Theorem 5).