Theorems · Theorem · commutative algebra

Algebra.TensorProduct.closure_range_union_range_eq_top

∀ (R : Type uR) (A : Type uA) (B : Type uB) [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Ring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B],
  Subring.closure (Set.range ⇑Algebra.TensorProduct.includeLeft ∪ Set.range ⇑Algebra.TensorProduct.includeRight) = ⊤

Defined in: Mathlib.RingTheory.TensorProduct.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Ring Ring Algebra Algebra

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Cites24

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Top.topstatement and proof · cited by 9,680
Ringstatement and proof · cited by 7,463
Set.rangestatement and proof · cited by 4,705
mul_oneproof · cited by 3,885
AlgHomstatement · cited by 3,236
one_mulproof · cited by 2,841
TensorProductstatement and proof · cited by 2,545
TensorProduct.tmulproof · cited by 1,182

Cited by1

Results whose statement or proof uses this declaration.

CommRingCat.closure_range_union_range_eq_top_of_isPushoutproof · cited by 1