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Theorems · Theorem · commutative algebra

IsLocalization.subsingleton

∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} {S : Type u_2} [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] [IsLocalization M S], 0 ∈ M → Subsingleton S

If M contains 0 then the localization at M is trivial.

Defined in
Mathlib.RingTheory.Localization.Defs
Cited by
1 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiringAlgebraIsLocalization
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Around this declaration

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HomogeneousLocalization.subsingleton · cited by 5HomogeneousLocalization.s…Algebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringSubmonoid · cited by 3086SubmonoidIsLocalization · cited by 636IsLocalizationIsLocalization.toLocalizationMap · cited by 69IsLocalization.toLocaliza…Submonoid.LocalizationMap.subsingleton · cited by 2LocalizationMap.subsingle…IsLocalization.subsingletonCITED BYCITES

Cites6

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Cited by1

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