Ideals in free modules over PIDs #
Main results #
S ⧸ I, if
Sis finite free as a module over a PID
R, can be written as a product of quotients of
Rby principal ideals.
We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
Ideal quotients over a free finite extension of
ℤ are isomorphic to a direct product of
A nonzero ideal over a free finite extension of
ℤ has a finite quotient.
Can't be an instance because of the side condition
I ≠ ⊥, and more importantly,
because the choice of
Fintype instance is non-canonical.
S⧸I as a direct sum of cyclic
(quotients by the ideals generated by Smith coefficients of