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Let A be a Noetherian local ring of dimensiondand with maximal idealm. ThenAis called Buchsbaum if every system of parameters is a weak sequence. This is equivalent to the condition that, for every parameter idealq, the differenceis an invariantI(A) ofAnot depending on the choice ofq. (See Section 2 for the detail.) The concept of Buchsbaum rings was introduced by Stückrad and Vogel , and the theory of Buchsbaum singularities is now developing (cf. , , , , and ).doi:10.1017/s0027763000019073 fatcat:fhmt5na6jbczro6efhjictuo5q