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Theorems · Theorem · commutative algebra

Localization.cardinalMk

∀ {R : Type u} [inst : CommRing R] {S : Submonoid R},
  S ≤ nonZeroDivisors R → Cardinal.mk (Localization S) = Cardinal.mk R
Defined in
Mathlib.RingTheory.Localization.Cardinality
Cited by
1 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsLocalization.lift_cardinalMk · cited by 2IsLocalization.lift_cardi…CommRing · cited by 17173CommRingSubmonoid · cited by 3086SubmonoidCardinal · cited by 2598CardinalCardinal.mk · cited by 942Cardinal.mknonZeroDivisors · cited by 895nonZeroDivisorsLocalization · cited by 270LocalizationnonZeroDivisorsLeft_eq_nonZeroDivisors · cited by 4nonZeroDivisorsLeft_eq_no…OreLocalization.cardinalMk · cited by 1OreLocalization.cardinalMkLocalization.cardinalMkCITED BYCITES

Cites8

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Cited by1

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