Buchsbaum ring explained

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} )\colon a _{i)\subset(a} _{1, … ,a} _{i-1} ) for all i .

They were introduced by and are named after David Buchsbaum.

Every Cohen–Macaulay local ring is a Buchsbaum ring. Every Buchsbaum ring is a generalized Cohen–Macaulay ring.