Theorems · Theorem · commutative algebra
Subring.smul_mem_pointwise_smul_iff
∀ {M : Type u_1} {R : Type u_2} [inst : Group M] [inst_1 : Ring R] [inst_2 : MulSemiringAction M R] {a : M}
{S : Subring R} {x : R}, a • x ∈ a • S ↔ x ∈ S- Defined in
- Mathlib.Algebra.Ring.Subring.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupRingMulSemiringAction
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Cites6
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
- Groupstatement and proof · cited by 6,238
- Subringstatement and proof · cited by 602
- MulSemiringActionstatement and proof · cited by 423
- Subring.pointwiseMulActionstatement · cited by 23
- Set.smul_mem_smul_set_iffproof · cited by 14
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