In mathematics, especially in commutative algebra, certain prime ideals called minimal prime ideals play an important role in understanding rings and modules.
The notion of height and Krull's principal ideal theorem use minimal prime ideals.
A minimal prime ideal over an ideal I in a Noetherian ring R is precisely a minimal associated prime (also called isolated prime) of
All rings are assumed to be commutative and unital.
A Noetherian local ring
is said to be equidimensional if for each minimal prime ideal
See also equidimensional scheme and quasi-unmixed ring.