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Buchsbaum ring

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Source updated August 12, 2023

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 Jürgen Stückrad and Wolfgang Vogel (1973) and are named after David Buchsbaum.

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

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