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Theorems · Theorem · commutative algebra

RingHom.IsStandardSmooth.smooth

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S}, f.IsStandardSmooth → f.Smooth

Any standard smooth ring homomorphism is smooth.

Defined in
Mathlib.RingTheory.RingHom.LocallyStandardSmooth
Cited by
1 results in Mathlib
Foundations
Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRing
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Around this declaration

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

RingHom.smooth_iff_locally_isStandardSmooth · cited by 1RingHom.smooth_iff_locall…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomRingHom.toAlgebra · cited by 337RingHom.toAlgebraRingHom.Smooth · cited by 30RingHom.SmoothRingHom.IsStandardSmooth · cited by 16RingHom.IsStandardSmoothIsStandardSmooth.smoothCITED BYCITES

Cites6

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Cited by1

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