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We study a construction of Tchernev in which a complex of vector spaces is built from the structure of a finite lattice L. When L is the lcm-lattice of a monomial ideal I in the ring R = k[x_{1},…,x_{n}], this complex of vector spaces can be transfomed into a complex F of free multigraded modules that approximates the minimal free resolution of the module R/I. Further, we define the class of {lattice-linear} monomial ideals and show that F is the minimal free resolution of the module R/I if and only if I is lattice-linear.
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