  We study monomial ideals using the operation polarization to first turn them
into square-free monomial ideals. We focus on monomial ideals whose
polarization produce simplicial trees, and show that many of the properties of
simplicial trees hold for such ideals.This includes Cohen-Macaulayness of the
Rees ring, and being sequentially Cohen-Macaulay. The appendix is an
independent study of primary decomposition in a sequentially Cohen-Macaulay
module. We demonstrate how every submodule appearing in the filtration of a
sequentially Cohen-Macaulay module can be described in terms of the primary
decomposition of the 0-submodule.
