associated prime ideal

associated prime ideal

[ə′sō·sē‚ād·əd ′prīm ‚ī·dēl]
(mathematics)
A prime ideal I in a commutative ring R is said to be associated with a module M over R if there exists an element x in M such that I is the annihilator of x.
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Hence, p must contain some associated prime ideal p' of fB.
r] a primary decomposition of N in M with associated prime ideals [Mathematical Expression Omitted].
r] be a primary decomposition with associated prime ideals [p.
An ideal I of M is contracted with respect to the A-adic topology T if and only if A + P [not equal to] M holds for every associated prime ideal P of I.
When R is Noetherian, every prime ideal has finite height and the height of an arbitrary ideal is defined to be the minimum of the heights of its associated prime ideals.
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