Buchsbaum ring

In mathematics, Buchsbaum rings are Noetherian local rings such that every system of parameters is a weak sequence. A sequence $$(a_1,\cdots,a_r)$$ of the maximal ideal $$m$$ is called a weak sequence if $$ m\cdot((a_1,\cdots,a_{i-1})\colon a_i)\subset(a_1,\cdots,a_{i-1})$$ 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.