Theorems · Theorem · commutative algebra
TensorProduct.mk_surjective
∀ (R : Type u_1) (M : Type u_2) (S : Type u_3) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : Semiring S] [inst_4 : Algebra R S], Function.Surjective ⇑(algebraMap R S) → Function.Surjective ⇑((TensorProduct.mk R S M) 1)
- Defined in
- Mathlib.RingTheory.TensorProduct.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Submoduleproof · cited by 7,192
- Set.ofPredproof · cited by 6,101
Cited by4
Results whose statement or proof uses this declaration.
- Module.free_of_flat_of_isLocalRingproof · cited by 7
- IsLocalRing.map_tensorProduct_mk_eq_topproof · cited by 4
- TensorProduct.spanFinrank_top_eq_of_residueFieldproof · cited by 1
- Algebra.TensorProduct.includeRight_surjectiveproof · cited by 0