A criterion for regular sequences

Details A criterion for regular sequences A criterion for regular sequences

2004-06-28

arxiv.org/abs/math/0406566v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 2, May 2004, pp. 103-106

Mathematics

Algebraic Geometry

4 pages, no figures, no tables

Scientific paper

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 ${\rm V}(g_{1}, ..., g_{r}) \subseteq {\rm V} (f_{1}, >..., f_{r})$ 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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