On Buchsbaum rings

Abstract

Now recall some definition. The concept of Buchsbaum rings was given by Stiickrad and Vogel (cf. 114, 151) and has its root in an answer of Vogel [ 19 1 to a problem of Buchsbaum (cf. [2, p. 2281). Let A be a Noetherian local ring with maximal ideal m. Then A is called Buchsbaum if the difference I,(A,/q) e,(q) is an invariant Z(A) of A not depending on the particular choice of a parameter ideal 4 of A, where e,(q) denotes the multiplicity of A rclativc to q. Clearly the class of Buchsbaum local rings contains Cohen-Macaulay local rings, and it is known that they enjoy many good properties. For example, the local cohomology modules &(A) (0 < i < d = dim A) of a Buchsbaum local ring A are vector spaces over A/m and