David Buchsbaum

Buchsbaum ring

In mathematics, Buchsbaum rings are Noetherian local rings such that every system of parameters is a weak sequence. A sequence {\displaystyle (a_{1},\cdots ,a_{r})} of the maximal ideal m {\displaystyle m} is called a weak sequence if m ⋅ ( ( a 1 , ⋯ , a i − 1 ) : a i ) ⊂ ( a 1 , ⋯ , a i − 1 ) {\displaystyle m\cdot ((a_{1},\cdots ,a_{i-1})\colon a_{i})\subset (a_{1},\cdots ,a_{i-1})} for all i {\displaystyle i} .