Primary Decompositions of Regular Sequences

Abstract

Let $R$ be a Noetherian ring and $x_1,\dots ,x_t$ a permutable regular sequence of elements in $R$. Then there exists a finite set of primes $\Lambda$ and natural number $C$ so that for all $n_1,\dots ,n_t$ there exists a primary decomposition $(x_1^{n_1},\dots ,x_t^{n_t})=Q_1\cap \cdots \cap Q_{\ell }$ so that $\sqrt{Q_i}\in \Lambda$ and ${\sqrt{Q_i}}^{C(n_1+\cdots +n_t)}\subseteq Q_i$ for all $1\le i\le \ell$.

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