Theorems · Theorem · commutative algebra
Algebra.trace_trace
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] [Module.Free R S]
[Module.Finite R S] [Module.Free S T] [Module.Finite S T] (x : T),
(Algebra.trace R S) ((Algebra.trace S T) x) = (Algebra.trace R T) x- Defined in
- Mathlib.RingTheory.Trace.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 97 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.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- Module.Finitestatement and proof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- Module.Free.chooseBasisproof · cited by 121
- Algebra.tracestatement · cited by 90
- Algebra.trace_trace_of_basisproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- trace_eq_trace_adjoinproof · cited by 3
- Algebra.trace_eq_zero_of_not_isSeparableproof · cited by 2
- FractionalIdeal.smul_mem_dual_oneproof · cited by 1
- FractionalIdeal.trace_mem_dual_oneproof · cited by 1
- Algebra.trace_comp_traceproof · cited by 0