Some results on T-rough ideal on quotient Lie algebras

In this paper we introduce the lower inverse and upper inverse under set-valued homomorphism in a quotient Lie algebra. Moreover we show that L_T (H ⁄ I) and U_T (H ⁄ I) are ideals of L ⁄ I if H be an ideal of L. Also we study several homomorphisms between lower inverses.