Abstract
Let (R, 𝔪, k) be a regular local ring of dimension n and let M be a finite length R-module. Horrock's conjecture [2] says that the ith Betti number of M must be at least . The article “Betti Numbers of Modules of Exponent Two over Regular Local Rings,” by Shou-Te Chang [1], addresses the case that 𝔪2 M = 0. The purpose of the present article is to correct a few problems in the arguments in [1]. In particular, we will be analyzing certain Koszul matrices and systematically finding a maximal set of linearly independent columns of these matrices.
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