Title: Annihilators of Koszul Homologies and Almost Complete Intersections,
Abstract: In this article, we propound a question on the annihilator of Koszul
homologies of a system of parameters of an almost complete intersection $R$.
The question can be stated in terms of the acyclicity of certain (finite)
residual approximation complexes whose $0$-th homologies are the residue field
of $R$. We show that our question has an affirmative answer for certain almost
complete intersection rings with small multiplicities, as well as for the
$1$-th Koszul homology of any almost complete intersection. The statement about
the $1$-th Koszul homology is shown to be equivalent to the Monomial Conjecture
and thus follows from its validity.