Theorems · Theorem · commutative algebra
Algebra.isIntegral_trace
∀ {R : Type u_1} [inst : CommRing R] {L : Type u_5} [inst_1 : Field L] {F : Type u_6} [inst_2 : Field F]
[inst_3 : Algebra R L] [inst_4 : Algebra L F] [inst_5 : Algebra R F] [IsScalarTower R L F] [FiniteDimensional L F]
{x : F}, IsIntegral R x → IsIntegral R ((Algebra.trace L F) x)- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- Polynomial.mapproof · cited by 806
- minpolyproof · cited by 439
Cited by7
Results whose statement or proof uses this declaration.
- FractionalIdeal.dual_ne_zeroproof · cited by 5
- FractionalIdeal.le_dual_inv_auxproof · cited by 2
- IsIntegralClosure.range_le_span_dualBasisproof · cited by 2
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- Submodule.one_le_traceDual_oneproof · cited by 0
- Algebra.discr_isIntegralproof · cited by 0
- isIntegral_discr_mul_of_mem_traceDualproof · cited by 0