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[Merged by Bors] - feat(ring_theory/localization): order embedding of ideals, local ring instance #3287

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[Merged by Bors] - feat(ring_theory/localization): order embedding of ideals, local ring instance #3287

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101damnations
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sorry for the long break in PRs. This is the order embedding of ideals in a localization & the local ring instance on the localization at the complement of a prime ideal.

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The linter says /- The `fails_quickly` linter reports: -/ /- TYPE CLASS SEARCHES TIMED OUT. For the following classes, there is an instance that causes a loop, or an excessively long search.: -/ -- ring_theory/ideals.lean #print local_ring /- maximum class-instance resolution depth has been reached (the limit can be increased by setting option 'class.instance_max_depth') (the class-instance resolution trace can be visualized by setting option 'trace.class_instances') -/

I am not sure what to do about this - the local ring instance added in this PR compiles - should I increase class.instance_max_depth just before the local ring instance or something? I don't understand how this PR can affect ring_theory/ideals.lean as the linter seems to imply

jcommelin
jcommelin reviewed Jul 4, 2020
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Looks good to me! Maybe the instance is tripping up because codomain is reducible? I have no idea. @gebner could you please take a look?

src/ring_theory/localization.lean Outdated
namespace ideal

/-- The complement of a prime ideal `I ⊆ R` is a submonoid of `R`. -/
def prime_submonoid :
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Suggested change
def prime_submonoid :
def prime_complement :

Otherwise it sounds like you're turning the prime ideal itself into a submonoid.

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good point... What about prime_compl, to be in keeping with set.compl etc?

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yup, sounds good to me

jcommelin
jcommelin reviewed Jul 4, 2020
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src/ring_theory/localization.lean Outdated
@[nolint unused_arguments has_inhabited_instance]
def codomain (f : localization_map M S) := S

instance : comm_ring f.codomain := _inst_2
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Suggested change
instance : comm_ring f.codomain := _inst_2
instance : comm_ring f.codomain := by apply_instance

_inst_2 doesn't seem like a very stable name. If someone adds a variable we might suddenly need _inst_3 here.

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fair point! by apply_instance doesn't work but I've just found out you can use by assumption for instances... awesome

Also thank you for the irreducible codomain appeasing the linter :)

src/ring_theory/localization.lean Outdated
def codomain (f : localization_map M S) := S

instance : comm_ring f.codomain := _inst_2
instance {K : Type*} [field K] (f : localization_map M K) : field f.codomain := _inst_4
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instance {K : Type*} [field K] (f : localization_map M K) : field f.codomain := _inst_4
instance {K : Type*} [field K] (f : localization_map M K) : field f.codomain := by apply_instance

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Thanks 🎉

bors merge

@github-actions github-actions bot added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Jul 4, 2020
bors bot pushed a commit that referenced this pull request Jul 4, 2020
@101damnations
feat(ring_theory/localization): order embedding of ideals, local ring…
023d4f7 
… instance (#3287)
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bors bot commented Jul 4, 2020

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(ring_theory/localization): order embedding of ideals, local ring instance [Merged by Bors] - feat(ring_theory/localization): order embedding of ideals, local ring instance Jul 4, 2020
@bors bors bot closed this Jul 4, 2020
@bors bors bot deleted the ring_loc_additions branch July 4, 2020 19:37
cipher1024 pushed a commit to cipher1024/mathlib that referenced this pull request Mar 15, 2022
@101damnations @cipher1024
feat(ring_theory/localization): order embedding of ideals, local ring…
c3038f3 
… instance (leanprover-community#3287)
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