Theorems · Theorem · commutative algebra
Algebra.isEpi_of_surjective_algebraMap
∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A], Function.Surjective ⇑(algebraMap R A) → Algebra.IsEpi R A
See also Algebra.isEpi_iff_surjective_algebraMap_of_finite.
- Defined in
- Mathlib.Algebra.Algebra.Epi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- TensorProductproof · cited by 2,545
- TensorProduct.tmulproof · cited by 1,182
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- TensorProduct.smul_tmulproof · cited by 33
- Algebra.IsEpistatement · cited by 18
- Algebra.isEpi_iff_forall_one_tmul_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.isEpi_iff_surjective_algebraMap_of_finiteproof · cited by 2