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The equation det(M)=0 defines a hypersurface singularity and the (co)-kernel of M is a maximally Cohen-Macaulay module over the local ring of this singularity.\n  Suppose the determinant det(M) is reducible, i.e. the hypersurface is locally reducible. A natural question is whether the matrix is equivalent to a block-diagonal or at least to an upper-block-triangular. (Or whether the corresponding module is decomposable or at least is an extension.) 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The equation det(M)=0 defines a hypersurface singularity and the (co)-kernel of M is a maximally Cohen-Macaulay module over the local ring of this singularity.\n  Suppose the determinant det(M) is reducible, i.e. the hypersurface is locally reducible. A natural question is whether the matrix is equivalent to a block-diagonal or at least to an upper-block-triangular. (Or whether the corresponding module is decomposable or at least is an extension.) 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