A criterion for regular sequences

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Let R be a commutative noetherian ring and f₁,..., fᵣ ∈ R. In this article we give (cf. the Theorem in 2) a criterion for f₁,..., fᵣ 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(g₁,..., gᵣ) V (f₁, >..., fᵣ) in Spec R and if f₁,..., fᵣ is a regular sequence in R, then g₁,..., gᵣ is also a regular sequence in R.