Theorems · Theorem · commutative algebra
IsIntegral.of_mul_unit
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] {x y : B} {r : R},
(algebraMap R B) r * y = 1 → IsIntegral R (x * y) → IsIntegral R x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- Polynomial.aevalproof · cited by 615
- Polynomial.Monicproof · cited by 461
- IsIntegralstatement and proof · cited by 427
Cited by2
Results whose statement or proof uses this declaration.
- isIntegral_localizationproof · cited by 4
- RingHom.IsIntegralElem.of_mul_unitproof · cited by 1