Theorems · Theorem · commutative algebra
Ideal.cardQuot_pow_inertiaDeg
∀ {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) [Module.Finite R S] [p.IsMaximal] [q.IsMaximal] [q.LiesOver p],
Submodule.cardQuot p ^ q.inertiaDeg R = Submodule.cardQuot q- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 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.
- 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.Quotientproof · cited by 2,301
- Module.Finitestatement and proof · cited by 1,032
- 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
- Submodule.cardQuotstatement and proof · cited by 14
- Ideal.inertiaDeg'_algebraMapproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.absNorm_pow_inertiaDegproof · cited by 2
- Ideal.cardQuot_pow_inertiaDeg'proof · cited by 0