k-regular sequences to extension functors and local cohomology modules

Abstract

In this paper we generalize the Zero Divisor Conjecture and Rigidity Theorem for k-regular sequence. For this purpose for any k-regular M-sequence x₁, ..., x_n we prove that if , then , for all i ≥ 1. Also we show that if , then , for all integers i ≥ 0 (i ≠ n).