Theorems · Theorem · linear algebra
Submodule.tmul_mem_baseChange_of_mem
∀ {R : Type u_1} {M : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : AddCommMonoid M] [inst_4 : Module R M] {p : Submodule R M} (a : A) {m : M},
m ∈ p → a ⊗ₜ[R] m ∈ Submodule.baseChange A p- Cited by
- 6 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulstatement and proof · cited by 1,182
- Submodule.baseChangestatement · cited by 36
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.baseChange_topproof · cited by 5
- LieModule.lowerCentralSeries_one_inf_center_le_ker_traceFormproof · cited by 1
- LieSubmodule.tmul_mem_baseChange_of_memproof · cited by 1
- LieModule.isNilpotent_derivedSeries_of_traceForm_eq_zeroproof · cited by 1
- LieAlgebra.isSolvable_tensorProduct_iffproof · cited by 0
- Submodule.toBaseChange.toLinearEquiv_symm_applystatement · cited by 0