Commit 2022-05-02 15:58 64bc02c5
View on Github →feat(ring_theory/dedekind_domain): Chinese remainder theorem for Dedekind domains (#13067)
The general Chinese remainder theorem states R / I
is isomorphic to a product of R / (P i ^ e i)
, where P i
are comaximal, i.e. P i + P j = 1
for i ≠ j
, and the infimum of all P i
is I
.
In a Dedekind domain the theorem can be stated in a more friendly way, namely that the P i
are the factors (in the sense of a unique factorization domain) of I
. This PR provides two ways of doing so, and includes some more lemmas on the ideals in a Dedekind domain.