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Theorems · Theorem · commutative algebra

Algebra.IsStandardOpenImmersion.trans

∀ (R : Type u_1) (S : Type u_2) (T : Type u_3) [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : CommSemiring T] [inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T]
  [Algebra.IsStandardOpenImmersion R S] [Algebra.IsStandardOpenImmersion S T], Algebra.IsStandardOpenImmersion R T
Defined in
Mathlib.RingTheory.RingHom.OpenImmersion
Cited by
2 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiringCommSemiringAlgebraAlgebraAlgebraIsScalarTowerAlgebra.IsStandardOpenImmersionAlgebra.IsStandardOpenImmersion
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Algebra.IsLocalIso.trans · cited by 1IsLocalIso.transRingHom.IsStandardOpenImmersion.comp · cited by 1IsStandardOpenImmersion.c…DFunLike.coe · cited by 62936DFunLike.coeAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringAlgebra.algebraMap · cited by 4706Algebra.algebraMapIsScalarTower · cited by 3896IsScalarTowerIsLocalization.Away · cited by 218IsLocalization.AwayAssociated.symm · cited by 87Associated.symmAlgebra.IsStandardOpenImmersion · cited by 16Algebra.IsStandardOpenImm…IsLocalization.Away.sec · cited by 9Away.secIsLocalization.Away.mul' · cited by 7Away.mul'IsLocalization.Away.of_associated · cited by 6Away.of_associatedAlgebra.IsStandardOpenImmersion.exists_away · cited by 2IsStandardOpenImmersion.e…IsLocalization.Away.associated_sec_fst · cited by 2Away.associated_sec_fstIsStandardOpenImmersion.transCITED BYCITES

Cites13

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Cited by2

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