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 Abstract: In this paper, study the module structure of ${\rm Ext}_{BP_*BP}^0(BP_*, BP_*/(p , v_1^\infty , v_2^\infty )),$ which is regarded as the chromatic $E_1$-term converging to the second line of the Adams-Novikov $E_2$-term for the Moore spectrum. The main difficulty here is to construct elements $x(sp^r/j;k)$ from the Miller-Ravenel-Wilson elements $(x_{3,r}^s/v_2^j)^{p^k} \in H^0M_2^1$. We achieve this by developing some inductive methods of constructing $x(sp^r/j;k)$ on $k$. Author information: Department of Mathematics, Faculty of Science, Osaka City University nakai@sci.osaka-cu.ac.jp http://www.sci.osaka-cu.ac.jp/~nakai/