A criterion for regular sequences

2004/06/28 by D P Patil, U Storch, J Stuckrad
Mathematics · #math.AG

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 2, May 2004, pp. 103-106 · 4 pages, no figures, no tables

arxiv created 2004/06/28 · arxiv updated 2009/12/01

Abstract

Let R be a commutative noetherian ring and f₁, ..., f_r ∈ R. In this article we give (cf. the Theorem in \S2) a criterion for f₁, ..., f_r to be regular sequence for a finitely generated module over R which strengthens and generalises a result in \cite2. As an immediate consequence we deduce that if \rm V(g₁, ..., g_r) ⊆ \rm V (f₁, >..., f_r) in Spec R and if f₁, ..., f_r is a regular sequence in R, then g₁, ..., g_r is also a regular sequence in R.

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