Theorems · Theorem · commutative algebra
Subring.mem_smul_pointwise_iff_exists
∀ {M : Type u_1} {R : Type u_2} [inst : Monoid M] [inst_1 : Ring R] [inst_2 : MulSemiringAction M R] (m : M) (r : R)
(S : Subring R), r ∈ m • S ↔ ∃ s ∈ S, m • s = r- Defined in
- Mathlib.Algebra.Ring.Subring.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidRingMulSemiringAction
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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
- Monoidstatement and proof · cited by 3,887
- Subringstatement and proof · cited by 602
- MulSemiringActionstatement and proof · cited by 423
- Subring.pointwiseMulActionstatement · cited by 23
- Set.mem_smul_setproof · cited by 16
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