Theorems · Theorem · commutative algebra
Ideal.pointwise_smul_toAddSubgroup
∀ {M : Type u_1} [inst : Monoid M] {R : Type u_4} [inst_1 : Ring R] [inst_2 : MulSemiringAction M R] (a : M)
(S : Ideal R), (Function.Surjective fun r => a • r) → Submodule.toAddSubgroup (a • S) = a • Submodule.toAddSubgroup S- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidRingMulSemiringAction
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Monoidstatement and proof · cited by 3,887
- AddSubgroupstatement · cited by 3,232
- MulSemiringActionstatement and proof · cited by 423
- Submodule.toAddSubgroupstatement · cited by 106
- AddSubgroup.extproof · cited by 75
- Ideal.pointwiseDistribMulActionstatement · cited by 56
- AddSubgroup.pointwiseMulActionstatement · cited by 24
- MulSemiringAction.toRingHomproof · cited by 23
- Ideal.mem_map_iff_of_surjectiveproof · cited by 19
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