In mathematics, a system of parameters for a local Noetherian ring of Krull dimension d with maximal ideal m is a set of elements x1, ..., xd that satisfies any of the following equivalent conditions: Every local Noetherian ring admits a system of parameters.
[1] It is not possible for fewer than d elements to generate an ideal whose radical is m because then the dimension of R would be less than d. If M is a k-dimensional module over a local ring, then x1, ..., xk is a system of parameters for M if the length of M / (x1, ..., xk) M is finite.
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