The Buchsbaum-Eisenbud Theorem states that a finitely generated module over a Cohen-Macaulay ring can be decomposed into a direct sum of modules that reflect the structure of the ring and its associated primes. This theorem highlights the relationship between the algebraic properties of Cohen-Macaulay rings and their geometric features, particularly in terms of shellability, which involves the combinatorial structure of simplicial complexes associated with these rings.
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