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searching for System of parameters 8 found (14 total)

Regular local ring (1,889 words) [view diff] exact match in snippet view article find links to article

n {\displaystyle a_{1},\ldots ,a_{n}} are then called a regular system of parameters. Let k = A / m {\displaystyle k=A/{\mathfrak {m}}} be the residue

Monomial conjecture (124 words) [view diff] exact match in snippet view article find links to article

Noetherian local ring of Krull dimension d and let x1, ..., xd be a system of parameters for A (so that A/(x1, ..., xd) is an Artinian ring). Then for all

Generalized Cohen–Macaulay ring (406 words) [view diff] exact match in snippet view article find links to article

{\mathfrak {m}}} -primary ideal Q {\displaystyle Q} such that for each system of parameters x 1 , … , x d {\displaystyle x_{1},\dots ,x_{d}} in Q {\displaystyle

Glossary of commutative algebra (9,772 words) [view diff] exact match in snippet view article find links to article

In particular a big Cohen–Macaulay module is a module that has a system of parameters for which it is regular. Boolean ring A Boolean ring is a ring such

Principles and parameters (2,088 words) [view diff] exact match in snippet view article find links to article

of explanatory adequacy. Particularly, a systematic, predictive system of parameters, their properties and interactions, along the lines of the periodic

Rees decomposition (160 words) [view diff] exact match in snippet view article find links to article

is a homogeneous element and the d elements θi are a homogeneous system of parameters for R and ηαk[θfα+1,...,θd] ⊆ k[θ1, θfα]. Stanley decomposition Hironaka

Dimension theory (algebra) (6,961 words) [view diff] exact match in snippet view article

k=R/(f_{1},\dots ,f_{n})} , f i {\displaystyle f_{i}} a regular system of parameters. An exact sequence 0 → M → f M → M 1 → 0 {\displaystyle 0\to M{\overset

Hironaka decomposition (676 words) [view diff] exact match in snippet view article find links to article

{\displaystyle R_{0}=K} admits a (not necessarily unique) homogeneous system of parameters (HSOP). A HSOP (also termed primary invariants) is a set of homogeneous