Theorems · Theorem · linear algebra
Submodule.baseChange_eq_span
∀ {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),
Submodule.baseChange A p = Submodule.span A ↑(Submodule.map ((TensorProduct.mk R A M) 1) p)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- 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
- LinearMapstatement · cited by 10,215
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- mul_oneproof · cited by 3,885
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.baseChange_botproof · cited by 2
- Submodule.baseChange_spanproof · cited by 2
- LieSubmodule.mem_baseChange_iffproof · cited by 1
- Algebra.TensorProduct.adjoin_one_tmul_image_eq_topproof · cited by 0