= Solution
A <minimal primary decomposition> is a finite expression
$$
\boxed{I=\bigcap_{j=1}^t\mathfrak q_j}
$$
in proper <primary ideals> such that the <prime ideals> $\mathfrak p_j=\sqrt{\mathfrak q_j}$ are pairwise distinct and no <primary ideal> can be omitted. More explicitly, for every $j$,
$$
\bigcap_{i\ne j}\mathfrak q_i\not\subseteq\mathfrak q_j.
$$
Thus minimality means both irredundancy and distinct <radicals of ideals>; it does not assert that the <primary ideals> themselves are uniquely determined. For $I=R$, one may use the empty intersection convention.
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