Theorems · Theorem · commutative algebra
IsLocalRing.basisQuotient_apply
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : IsLocalRing R] [inst_4 : Module.Finite R S] [inst_5 : Module.Free R S] {ι : Type u_3} [inst_6 : Fintype ι]
(b : Module.Basis ι R S) (i : ι),
(IsLocalRing.basisQuotient b) i = (Ideal.Quotient.mk (Ideal.map (algebraMap R S) (IsLocalRing.maximalIdeal R))) (b i)- Defined in
- Mathlib.RingTheory.LocalRing.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Module.Basisstatement and proof · cited by 1,477
- Module.Finitestatement and proof · cited by 1,032
- Ideal.mapstatement and proof · cited by 692
- Ideal.Quotient.mkstatement and proof · cited by 610
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.trace_quotient_mkproof · cited by 1
- IsLocalRing.basisQuotient_reprproof · cited by 1