Theorems · Theorem · ring theory
star_rat_smul
∀ {R : Type u_1} [inst : AddCommGroup R] [inst_1 : StarAddMonoid R] [inst_2 : Module ℚ R] (q : ℚ) (x : R),
star (q • x) = q • star xNote that this lemma holds for an arbitrary ℚ-action, rather than merely one coming from a
DivisionRing. We keep both the qsmul and rat_smul naming conventions for discoverability.
See star_qsmul.
- Defined in
- Mathlib.Algebra.Star.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Star.starstatement · cited by 1,082
- StarAddMonoidstatement and proof · cited by 296
- starAddEquivproof · cited by 25
- map_rat_smulproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- star_qsmulproof · cited by 0
- Matrix.conjTranspose_rat_smulproof · cited by 0