A Criterion for Regular Sequences

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

[学科分类] 数学（综合）

[关键词] Regular sequence.