Theorems · Theorem · commutative algebra
Polynomial.map_under_lt_comap_of_weaklyQuasiFiniteAt
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(f : Polynomial R →ₐ[R] S) (P : Ideal S) [inst_3 : P.IsPrime] [Algebra.WeaklyQuasiFiniteAt R P],
Ideal.map Polynomial.C (Ideal.under R P) < Ideal.comap (↑f) P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- le_reflproof · cited by 2,061
- Polynomial.Cstatement and proof · cited by 1,598
- Module.Finiteproof · cited by 1,032
- RingHom.compproof · cited by 899
- Ideal.IsPrimestatement and proof · cited by 827
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.map_under_lt_comap_of_quasiFiniteAtproof · cited by 0