Theorems · Theorem · commutative algebra
Ideal.inertiaDeg_eq_of_isMaximal
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
(q : Ideal S) [inst_3 : q.LiesOver p] [p.IsMaximal] [q.IsMaximal], q.inertiaDeg R = Module.finrank (R ⧸ p) (S ⧸ q)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Fieldproof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Module.finrankstatement · cited by 1,770
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.inertiaDegstatement · cited by 60
- Ideal.Quotient.fieldproof · cited by 25
- Ideal.inertiaDeg_eq_of_isFractionRingproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.inertiaDeg'_eq_inertiaDegproof · cited by 2
- NumberField.InfinitePlace.inertiaDeg_eq_finrankproof · cited by 2
- Ideal.inertiaDeg'_eq_of_isMaximalproof · cited by 0