Theorems · Theorem · field theory
IntermediateField.sup_toSubalgebra_of_isAlgebraic_right
∀ {K : Type u_3} {L : Type u_4} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
(E1 E2 : IntermediateField K L) [Algebra.IsAlgebraic K ↥E2],
(E1 ⊔ E2).toSubalgebra = E1.toSubalgebra ⊔ E2.toSubalgebra- Cited by
- 6 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringproof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringproof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerproof · cited by 3,896
- Subalgebrastatement and proof · cited by 1,353
- IntermediateFieldstatement and proof · cited by 988
- Algebra.adjoinproof · cited by 535
- IntermediateField.adjoinproof · cited by 382
- Algebra.IsAlgebraicstatement and proof · cited by 322
- IntermediateField.toSubalgebrastatement and proof · cited by 134
Cited by6
Results whose statement or proof uses this declaration.
- IntermediateField.sup_toSubalgebra_of_isAlgebraicproof · cited by 3
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_leftproof · cited by 2
- Submodule.traceDual_le_span_map_traceDualproof · cited by 2
- IntermediateField.LinearDisjoint.trace_algebraMapproof · cited by 1
- IntermediateField.LinearDisjoint.norm_algebraMapproof · cited by 0
- IntermediateField.sup_toSubalgebra_of_rightproof · cited by 0