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For the class of matrices over a field, the notion of 'rank of a matrix' as defined by 'the dimension of subspace generated by columns of that matrix' is folklore and cannot be generalized to the class of matrices over an arbitrary commutative ring. The 'determinantal rank' defined by the size of largest submatrix having nonzero determinant, which is same as the column rank of given matrix when the commutative ring under consideration is a field, was considered to be the best alternative fordoi:10.13001/1081-3810.3671 fatcat:6h5pxr5nevcklja5iizu3bqlgm