Theorems · Theorem · commutative algebra
Submodule.restrictScalars_top
∀ (S : Type u_1) (R : Type u_2) (M : Type u_3) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Semiring S] [inst_3 : Module S M] [inst_4 : Module R M] [inst_5 : SMul S R] [inst_6 : IsScalarTower S R M], Submodule.restrictScalars S ⊤ = ⊤
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- Submodule.restrictScalarsstatement · cited by 180
Cited by9
Results whose statement or proof uses this declaration.
- Module.Finite.transproof · cited by 16
- AdicCompletion.pow_smul_top_eq_ker_evalproof · cited by 4
- exists_subalgebra_of_fgproof · cited by 1
- KaehlerDifferential.map_surjective_of_surjectiveproof · cited by 1
- IsLocalRing.quotient_span_eq_top_iff_span_eq_topproof · cited by 1
- IsLocalRing.rank_cotangentSpace_eq_spanrank_maximalIdeal_of_fgproof · cited by 1
- Algebra.Extension.Cotangent.finiteproof · cited by 1
- Module.Finite.rightproof · cited by 1
- RingTheory.Sequence.isRegular_cons_iff'proof · cited by 1