Shuang LIANG, Li Ming TANG
In this paper, we first introduce the concepts of weak $c$-ideals, weak $c$-simple Lie superalgebras and weak $c$-ideals complementability of Lie superalgebras, and investigate some structural properties related to weak $c$-ideals over the fields with characteristics other than $2$, $3$; Secondly, the necessary and sufficient conditions for a Lie superalgebras to be a weak $c$-simple Lie superalgebras are given. By using $\rm{Frattini}$ ideals, the sufficient and necessary conditions for a weak $c$-ideal of a Lie superalgebra to be its ideal are given, and the necessary and sufficient conditions for its quotient subalgebra to have subideal complement are given; Finally, by using some weak $c$-ideals of a class of Lie superalgebras over fields with characteristic zero, the sufficient conditions for the class of Lie superalgebras to be solvable are given.