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تسجيل مستخدم جديدModules with Pure Resolutions
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We show that the property of a standard graded algebra R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module corresponding to any degree sequence of length at most depth(R). We also give a relation in terms of graded Betti numbers, called the Herzog-Kuhl equations, for a pure R-module M to satisfy the condition dim(R) - depth(R) = dim(M) - depth(M). When R is Cohen-Macaulay, we prove an analogous result characterizing all graded Cohen-Macaulay R-modules.
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Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we introduce and study the notions of $S$-pure $S$-exact sequences and $S$-absolutely pure modules which extend the classical notions of pure exact seq
uences and absolutely pure modules. And then we characterize $S$-von Neumann regular rings and uniformly $S$-Noetherian rings using $S$-absolutely pure modules.
Minimal cellular resolutions of the edge ideals of cointerval hypergraphs are constructed. This class of d-uniform hypergraphs coincides with the complements of interval graphs (for the case d=2), and strictly contains the class of `strongly stable h
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In this memoir, we give a completely constructive version of the celebrate book Finite Free Resolutions by Northcott, and of some other results related to the depth `a la Hochster, the Cayley complexes and their determinants, and the finite projective resolutions.
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