Theorems · Theorem · commutative algebra
IsAlgebraic.of_mul
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [NoZeroDivisors R]
{y z : S}, y ∈ nonZeroDivisors S → IsAlgebraic R y → IsAlgebraic R (y * z) → IsAlgebraic R z- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.adjoinproof · cited by 535
- Algebra.smul_defproof · cited by 287
- IsAlgebraicstatement and proof · cited by 163
- mul_right_commproof · cited by 108
- mem_nonZeroDivisors_of_ne_zeroproof · cited by 34
Cited by4
Results whose statement or proof uses this declaration.
- Complex.isAlgebraic_cos_rat_mul_piproof · cited by 1
- Complex.isAlgebraic_sin_rat_mul_piproof · cited by 1
- Real.isAlgebraic_sin_rat_mul_piproof · cited by 0
- Real.isAlgebraic_cos_rat_mul_piproof · cited by 0