A Criterion for Regular Sequences

Proceedings Mathematical Sciences

U Storch³  J Stückrad¹  D P Patil² 

[1] Fakultät für Mathematik und Informatik, Universität, Leipzig, D-00 Leipzig, Germany$$;Department of Mathematics, Indian Institute of Science, Bangalore 0 0, India$$;Fakultät für Mathematik, Ruhr Universität Bochum, D-0 Bochum, Germany$$

关键词: Regular sequence.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 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.

【 授权许可】

Unknown