Theorems · Theorem · commutative algebra
Submodule.baseChange_le_iff
∀ {R : Type u_1} {M : Type u_2} {A : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A]
[Module.FaithfullyFlat R A] [inst_4 : AddCommGroup M] [inst_5 : Module R M] {p q : Submodule R M},
Submodule.baseChange A p ≤ Submodule.baseChange A q ↔ p ≤ q- Cited by
- 0 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapproof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement and proof · cited by 2,545
- HasQuotient.Quotientproof · cited by 2,301
- LinearMap.compproof · cited by 1,642
- LinearMap.rangeproof · cited by 893
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.baseChangeOrderEmbeddingproof · cited by 3