Buchsbaum ring

In mathematics, Buchsbaum rings are Noetherian local rings such that every system of parameters is a weak sequence. A sequence ( a 1 , ⋯ , a r ) of the maximal ideal m is called a weak sequence if m ⋅ ( ( a 1 , ⋯ , a i − 1 ) : a i ) ⊂ ( a 1 , ⋯ , a i − 1 ) for all i .

They were introduced by Jürgen Stückrad and Wolfgang Vogel (1973) and are named after David Buchsbaum.

Every Cohen–Macaulay local ring is a Buchsbaum ring.