Theorems · Theorem · commutative algebra
minpoly.prime_of_isIntegrallyClosed
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [IsDomain R] [inst_3 : Algebra R S]
[IsIntegrallyClosed R] [IsDomain S] [Module.IsTorsionFree R S] {x : S}, IsIntegral R x → Prime (minpoly R x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- IsUnitproof · cited by 1,602
- Module.IsTorsionFreestatement and proof · cited by 600
- minpolystatement and proof · cited by 439
- IsIntegralstatement and proof · cited by 427
- Primestatement · cited by 277
- IsIntegrallyClosedstatement and proof · cited by 203
- ne_of_ltproof · cited by 203
- minpoly.monicproof · cited by 81
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.adjoin.powerBasis'_minpoly_genproof · cited by 0