Theorems · Theorem · commutative algebra
Subring.smul_sup
∀ {M : Type u_1} {R : Type u_2} [inst : Monoid M] [inst_1 : Ring R] [inst_2 : MulSemiringAction M R] (a : M)
(S T : Subring R), a • (S ⊔ T) = a • S ⊔ a • T- Defined in
- Mathlib.Algebra.Ring.Subring.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidRingMulSemiringAction
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MulSemiringAction.toRingHomproof · cited by 23
- Subring.map_supproof · cited by 2
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