Let $ I = (f_1, f_2); J = (g_1, g_2), L= (h_1, h_2) $ be monomial ideals in polynomial ring $ S = \mathbb{K}[x_1,...,x_n] $ such that $ f_1, f_2, g_1, g_2, h_1, h_2 \in S, f_1 $ and $ f_2 $, $ g_1 $ and $ g_2 $, $ h_1 $ and $ h_2 $ don't contain the same variables.
Find out the relationship between simplicial complex of $ I, J, L $ and simplicial complex of the product $ IJL $
i thinhk we need to find the polarization of $IJL$. Help me show this, please!
