Theorems · Theorem · commutative algebra
Subring.smul_closure
∀ {M : Type u_1} {R : Type u_2} [inst : Monoid M] [inst_1 : Ring R] [inst_2 : MulSemiringAction M R] (a : M)
(s : Set R), a • Subring.closure s = Subring.closure (a • s)- Defined in
- Mathlib.Algebra.Ring.Subring.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidRingMulSemiringAction
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Ringstatement and proof · cited by 7,463
- Monoidstatement and proof · cited by 3,887
- Set.smulSetstatement · cited by 608
- Subringstatement · cited by 602
- MulSemiringActionstatement and proof · cited by 423
- Subring.closurestatement · cited by 78
- Subring.pointwiseMulActionstatement · cited by 23
- MulSemiringAction.toRingHomproof · cited by 23
- RingHom.map_closureproof · cited by 4
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