A note on quasi-Buchsbaum rings

Source abstract

In this paper the ubiquity of non-Buchsbaum but quasi-Buchsbaum rings is established. The result is stated as follows: Let d ≥ 3 d \ge 3 and h 1 , h 2 , … , h d − 1 ≥ 0 {h_1},{h_2}, \ldots ,{h_{d - 1}} \ge 0 be integers and assume that at least two of h i {h_i} ’s are positive. Then there exists a non-Buchsbaum but quasi-Buchsbaum local integral domain A A of dim ⁡ A = d \dim A = d and such that l A ( H m i ( A ) ) = h i {l_A}(H_m^i(A)) = {h_i} for all 1 ≤ i ≤ d − 1 1 \le i \le d - 1 . Moreover if h 1 = 0 {h_1} = 0 the ring A A can be chosen to be normal.