On the canonical element conjecture. II (Q1340932)

[For part I see Trans. Am. Math. Soc. 299, 803-811 (1987; Zbl 0611.13011).] The main two theorems of this paper are the following: Theorem 1. Let \((A,m,k)\) be a noetherian local ring and let \(J_ i = \text{ann}_ A H_ m^{n-i} (A)\). Then for any nonzero \(x \in mJ_ 1J_ 2 \dots J_ r\), \(A/xA\) satisfies the canonical element conjecture (here \(r = \dim A - \text{depth} A)\). Theorem 2. Let \(x_ n \in J_ 1J_ 2 \dots J_ r\). Then for any s.o.p. \(x_ 1, x_ 2, \dots, x_ n\) of \(A\), \(x^ t_ 1, x_ 2^ t, \dots, x^ t_ n + x\) satisfies the canonical element conjecture in \(B = A[[X]]/(X^ 2)\) \((x\) denoting the image of \(X\) in \(B)\) for every positive integer \(t\).