Theorems · Theorem · commutative algebra
IsAlgebraic.of_smul
∀ {R : Type u_1} {A : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {z : A} {y : R},
y ∈ nonZeroDivisors R → IsAlgebraic R (y • z) → IsAlgebraic R z- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 1 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.
Cites18
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
- Submonoidstatement · cited by 3,086
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- nonZeroDivisorsstatement and proof · cited by 895
- Polynomial.aevalproof · cited by 615
- Algebra.smul_defproof · cited by 287
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgebraic.of_mulproof · cited by 4