Commit 2020-06-08 13:54 a7930425
View on Github →feat(ring_theory/fractional_ideal): pushforward of fractional ideals (#2984)
Extend submodule.map
to fractional ideals by showing that the pushforward is also fractional.
For this, we need a slightly tweaked definition of fractional ideal: if we localize R
at the submonoid S
, the old definition required a nonzero x : R
such that xI ≤ R
, and the new definition requires x ∈ S
instead. In the most common case, S = non_zero_divisors R
, the results are exactly the same, and all operations are still the same.
A practical use of these pushforwards is included: canonical_equiv
states fractional ideals don't depend on choice of localization map.