Theorems · Theorem · commutative algebra
IsIntegral.mul
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {x y : A},
IsIntegral R x → IsIntegral R y → IsIntegral R (x * y)- Cited by
- 24 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Algebra.algebraMapproof · cited by 4,706
- IsIntegralstatement and proof · cited by 427
- RingHom.IsIntegralElem.mulproof · cited by 4
Cited by25
Results whose statement or proof uses this declaration.
- integralClosureproof · cited by 105
- IsAlgebraic.mulproof · cited by 5
- IsLocalization.integralClosureproof · cited by 3
- IsIntegralClosure.range_le_span_dualBasisproof · cited by 2
- dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- PowerBasis.repr_mul_isIntegralproof · cited by 1
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1
- Algebra.dvd_algebraMap_intNorm_selfproof · cited by 1
- Polynomial.isIntegral_coeff_of_factorsproof · cited by 1