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Abstract: The problem of completing a k x n matrix with k < n to an n x n matrix with appropriate determinant has a long history, beginning with Hermite in 1849. We continue the study of this matrix completion problem over various commutative rings. Then we use these results to extend a 1997 result of Richter and Wardlaw for good matrices. This is joint work with William H. Gustafson, R. Bruce Richter, and Donald W. Robinson.