A primary ideal is an ideal 
such that if 
, then either 
or 
for some 
. Prime ideals are always
primary. A primary decomposition expresses any ideal 
as an intersection of primary ideals.
Primary Ideal
See also
Ideal, Prime IdealThis entry contributed by Bhuvanesh Bhatt
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Bhatt, Bhuvanesh. "Primary Ideal." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PrimaryIdeal.html