In mathematics, Buchsbaum rings are Noetherian

local ring In abstract algebra, more specifically ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic n ...

s 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_)\colon
a_i)\subset(a_1,\cdots,a_)

for all

i

. They were introduced by and are named after

David Buchsbaum David Alvin Buchsbaum (November 6, 1929 – January 8, 2021) was a mathematician at Brandeis University who worked on commutative algebra, homological algebra, and representation theory. He proved the Auslander–Buchsbaum formula and the Ausland ...

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

References

* * * * Commutative algebra Ring theory {{abstract-algebra-stub