Given a 0-dimensional affine K-algebra R=K[x1,…,xn]∕I, where I is an ideal in polynomial ring K[x1,…,xn] over field K, or, equivalently, given scheme, we construct effective algorithms for checking whether R complete intersection at maximal ideal, locally intersection, and strict intersection. These are based on Wiebe’s characterization of local intersections via the 0-th Fitting ideal. They al...