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isPrimary -- determine whether a submodule is primary



Checks to see if a given submodule Q of a module M is primary, i.e. whether or not M/Q has exactly one associated prime (which is equivalent for finitely generated modules over Noetherian rings). If the input is a single ideal, then the ambient module is taken to be the ring (i.e. the free module of rank 1), and does not need to be specified.

i1 : Q = ZZ/101[x,y,z]

o1 = Q

o1 : PolynomialRing
i2 : isPrimary ideal(y^6)

o2 = true
i3 : isPrimary(ideal(y^6), ideal(y))

o3 = true
i4 : isPrimary ideal(x^4, y^7)

o4 = true
i5 : isPrimary ideal(x*y, y^2)

o5 = false

See also

Ways to use isPrimary :

For the programmer

The object isPrimary is a method function with options.