Theorems · Theorem · commutative algebra
IsScalarTower.restrictScalars
∀ (R : Type u_1) (S : Type u_2) (M : Type u_3) [inst : Semiring S] [inst_1 : AddCommMonoid M] [inst_2 : CommSemiring R] [inst_3 : Algebra R S] [inst_4 : Module S M], IsScalarTower R S M
Module.restrictScalars forms a scalar tower.
- Defined in
- Mathlib.Algebra.Algebra.RestrictScalars
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- IsScalarTowerstatement · cited by 3,896
- Module.restrictScalarsstatement · cited by 3
- IsScalarTower.of_compHomproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- IsBaseChange.of_compproof · cited by 1
- Module.Dual.exists_extension_of_le_seminormproof · cited by 1
- LinearMap.IsSymmetric.restrictScalarsstatement · cited by 1
- ModuleCat.isScalarTower_of_algebra_moduleCatproof · cited by 0
- LinearMap.map_mul_of_map_mul_tmulproof · cited by 0