A criterion for regular sequences

Abstract

Let $R$ be a commutative noetherian ring and $f_1,...,f_r\in R$. In this article we give (cf. the Theorem in \S2) a criterion for $f_1,...,f_r$ to be regular sequence for a finitely generated module over $R$ which strengthens and generalises a result in \cite{2}. As an immediate consequence we deduce that if $\mathrm{V}(g_1,...,g_r)\subseteq \mathrm{V}(f_1,>...,f_r)$ in Spec $R$ and if $f_1,...,f_r$ is a regular sequence in $R$, then $g_1,...,g_r$ is also a regular sequence in $R$.

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