## Stream: maths

### Topic: Improve ring_theory/localization

#### Riccardo Brasca (Nov 24 2020 at 16:38):

Following a suggestion of @Johan Commelin (that is busy with other stuff) in #maths > Minimal polynomial over ℚ vs over ℤ I would like to improve ring_theory/localization. The problem is that is seems impossible (to me at least) or in any case very complicated to use results like gcd_domain_eq_field_fractions, where we have a monoid R with field of fractions K and an K-algebra L, in concrete situation, for example when R = ℤ. More precisely, I am not able to prove gcd_domain_eq_field_fractions in the case the GCD monoid is ℤ using gcd_domain_eq_field_fractions (of course redoing the proof in this case is easy).

I can do the "unskilled work", but I need some guidance. For example, Johan suggests that

is_localization (R A : Type*) [comm_ring R] [comm_ring A] [algebra R A] : Prop :=


should be a proposition. Should it be a structure? A class?

If someone wants so shed some light on what is needed to do for this kind of work any advice is very welcome!

Last updated: May 11 2021 at 17:39 UTC