In a Noetherian local ring of dimension , a list whose generated ideal has radical . Such lists exist, by successively avoiding the finitely many top-dimensional minimal primes. No list shorter than can generate a maximal-primary ideal, by the Krull height theorem.
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The term "system of parameters" can have different meanings depending on the context in which it's used. Here are a few possible interpretations across different fields: 1. **Mathematics and Statistics**: In the context of mathematical modeling or statistical analysis, a system of parameters refers to a set of variables that define a particular system or model. These parameters can influence the behavior of the system, and analyzing them can provide insights into the system's dynamics.