Theorems · Theorem · commutative algebra
Ring.mker_ordFrac_eq_isUnitSubmonoid
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {K : Type u_2}
[inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : IsFractionRing R K],
MonoidHom.mker (Ring.ordFrac R) = Submonoid.map (algebraMap R K) (IsUnit.submonoid R)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- Multiplicativestatement and proof · cited by 875
- IsFractionRingstatement and proof · cited by 738
- MonoidWithZeroHomstatement and proof · cited by 704
- WithZerostatement and proof · cited by 586
- Submonoid.mapstatement and proof · cited by 190
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