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We study the conjecture that, ifI,Jare μ −primary in a regular local ring (R, μ) with dim(R) = n, thenneeds at leastngenerators, and a related conjecture about the number of generators of the first Koszul homology module of an Artinian local ring (A,m). In this manuscript, we focus our attention on the complete intersection defect of the Artinian ring and its quotient by the Koszul elements. We prove that the number of generators of the first Koszul homology module ofx1,…,xn ∈ mon an Artinian local ring (A,m) is at least, where cidAdenotes the complete intersection defect of the Artinian local ringA. [ABSTRACT FROM PUBLISHER]