Theorems · Theorem · commutative algebra
Algebra.trace_prod_apply
∀ {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] [Module.Free R S] [Module.Free R T] [Module.Finite R S]
[Module.Finite R T] (x : S × T), (Algebra.trace R (S × T)) x = (Algebra.trace R S) x.1 + (Algebra.trace R T) x.2- Defined in
- Mathlib.RingTheory.Trace.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- LinearMap.compproof · cited by 1,642
- Module.Finitestatement and proof · cited by 1,032
- Module.Endproof · cited by 774
- Module.Freestatement and proof · cited by 597
- AlgHom.toLinearMapproof · cited by 254
- LinearMap.comp.congr_simpproof · cited by 209
- Algebra.tracestatement · cited by 90
Cited by3
Results whose statement or proof uses this declaration.
- not_dvd_differentIdeal_of_isCoprime_of_isSeparableproof · cited by 2
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1
- Algebra.trace_prodproof · cited by 0