A generalization of Rejection Lemma of Drozd-Kirichenko

$K\Lambda\simeq K\otimes_{R}\Lambda$ , and let Ind $\Lambda$ denote the set of isomorphism classes of indecomposable left $\Lambda$ -lattices. For an overorder $\Gamma$ of $\Lambda$ in $\tilde{\Lambda}$, we may naturally consider Ind $\Gamma$ as a subset of Ind $\Lambda$ . A subset ,9“ of Ind $\Lambda$ will be called a rejectable subset if there is an overorder $\Gamma$ such that $\mathscr{L}=Ind\Lambda$ –Ind $\Gamma$ . The map $\Gamma\vdasharrow$ (Ind $\Lambda$ –Ind $\Gamma$) defines a bijection from the set of all overorders of $\Lambda$ onto the set of all rejectable subsets of Ind $\Lambda$ . Indeed, the inverse map is given by $\mathscr{L}->\Lambda(\mathscr{L})$ . Here, for any subset $\mathscr{L}$ of Ind $\Lambda,$ $\Lambda(\mathscr{L})$ is defined as the intersection $\bigcap_{L\in Ind\Lambda-9},$ $O_{l}(L)$ of the left multiplier $O_{l}(L)$ $:=$