Theorems · Theorem · commutative algebra
IsAlgebraic.mul
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [NoZeroDivisors R]
{a b : S}, IsAlgebraic R a → IsAlgebraic R b → IsAlgebraic R (a * b)- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- map_mulproof · cited by 1,137
- NoZeroDivisorsstatement and proof · cited by 545
- IsIntegralproof · cited by 427
- Algebra.smul_defproof · cited by 287
- mul_ne_zeroproof · cited by 178
- IsAlgebraicstatement and proof · cited by 163
- mul_mul_mul_commproof · cited by 65
- IsIntegral.mulproof · cited by 24
Cited by5
Results whose statement or proof uses this declaration.
- IsAlgebraic.of_mulproof · cited by 4
- AlgebraicIndependent.extendScalarsproof · cited by 4
- IsTranscendenceBasis.sumElim_compproof · cited by 1
- IsAlgebraic.powproof · cited by 0
- Complex.isAlgebraic_tan_rat_mul_piproof · cited by 0