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Theorems · Theorem · commutative algebra

Algebra.trace_self

∀ {R : Type u_1} [inst : CommRing R], Algebra.trace R R = LinearMap.id

The trace map from R to itself is the identity map.

Defined in
Mathlib.RingTheory.Trace.Defs
Cited by
1 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.trace_self_apply · cited by 1Algebra.trace_self_applyDFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingLinearMap · cited by 10215LinearMapone_smul · cited by 1374one_smulLinearMap.id · cited by 625LinearMap.idLinearMap.ext_ring · cited by 152LinearMap.ext_ringAlgebra.trace · cited by 90Algebra.traceFintype.card_unique · cited by 59Fintype.card_uniqueModule.Basis.singleton · cited by 15Basis.singletonAlgebra.trace_algebraMap_of_basis · cited by 2Algebra.trace_algebraMap_…Algebra.trace_selfCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.