Let R be a Noetherian local ring and m a positive integer. Let I be the ideal of R generated by the maximal minors of an m × (m + 1) matrix M with entries in R . Assuming that the grade of the ideal generated by the k-minors of M is at least m − k + 2 for 1 ≤ ∀k ≤ m , we will study the associated primes of I n for ∀n > 0 . Moreover, we compute the saturation of I n for 1 ≤ ∀n ≤ m in the case where R is a Cohen-Macaulay ring and the entries of M are powers of elements that form an sop for R .

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Let (R , m) be a Cohen-Macaulay local ring and Q a parameter ideal of R . Suppose that an acyclic complex F • of length 3 which is an R-free resolution of an ideal a of R is given. In this paper, we describe a concrete procedure to get an acyclic complex * F • of length 3 that becomes an R-free resolution of a : R Q . As an application, we compute the symbolic powers of ideals generated by maximal minors of certain 2 × 3 matrices. * The last author is supported by KAKENHI (23540042)

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