We consider a local (or standard graded) ring R R with ideals alttext="script upper I prime"> <mml:mrow class="MJX-TeXAtom-O...

We propose a notion of minimal free resolutions for differential modules, and we prove existence uniqueness results such resolutions. also take the first steps toward studying structure modules. Our main result in this direction explains sense which resolution module is deformation its homology; leads to structural that mirror classical theorems about

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...