On the Set of Associated Primes of a Local Cohomology Module

Assume R is a local Cohen–Macaulay ring. It is shown that AssR(HlI(R)) is finite for any ideal I and any integer l provided AssR(H2(x, y)(R)) is finite for any x, y R and AssR(H3(x1, x2, y)(R)) is finite for any y R and any regular sequence x1, x2 R. Furthermore it is shown that AssR(HlI(R)) is always finite if dim(R) ≤ 3. The same statement is even true for dim(R) ≤ 4 if R is almost factorial.