Theorems · Theorem · commutative algebra
IsIntegral.pair
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Ring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] {x : A × B}, IsIntegral R x.1 → IsIntegral R x.2 → IsIntegral R xAn element of a product algebra is integral if each component is integral.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.aevalproof · cited by 615
- Polynomial.Monicproof · cited by 461
- IsIntegralstatement and proof · cited by 427
- Polynomial.eval₂proof · cited by 267
Cited by1
Results whose statement or proof uses this declaration.
- IsIntegral.pair_iffproof · cited by 0