Ideal of Definition

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My question refers to following excerpt: https://stacks.math.columbia.edu/tag/00KQ

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What is here the "ideal of definition" at the red tagged line?

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Let $m$ be the radical of $R$. The ideal of definition $I$ satisfies: for some $\mu, m^{\mu}\subset I\subset m$.

This is defined in Matsumura's Commutative Ring Theory, p.97.