Theorems · Theorem · commutative algebra
Ideal.range_mul
∀ {R : Type u} [inst : CommSemiring R] (A : Type u_2) [inst_1 : CommSemiring A] [inst_2 : Module R A]
[inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A] (a : A),
((LinearMap.mul R A) a).range = Submodule.restrictScalars R (Ideal.span {a})- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Submodulestatement · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- Ideal.spanstatement and proof · cited by 948
- LinearMap.rangestatement · cited by 893
- Submodule.extproof · cited by 204
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.exact_mulQuot_quotOfMulproof · cited by 1
- Ideal.range_mul'proof · cited by 0