Theorems · Theorem · ring theory
Semiring.zero_mul
∀ {α : Type u} [self : Semiring α] (a : α), 0 * a = 0Zero is a left absorbing element for multiplication
- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddMonoid.toZerostatement · cited by 325
Cited by13
Results whose statement or proof uses this declaration.
- Semiring.extproof · cited by 5
- ModuleCat.extendScalarsComp_hom_app_one_tmulstatement · cited by 3
- CommCStarAlgebra.toStarRingstatement · cited by 2
- CStarAlgebra.mk.noConfusionstatement · cited by 0
- CStarAlgebra.casesOnstatement · cited by 0
- CommCStarAlgebra.casesOnstatement · cited by 0
- RCLike.casesOnstatement · cited by 0
- CommCStarAlgebra.recOnstatement · cited by 0
- RCLike.recOnstatement · cited by 0
- CommCStarAlgebra.mk.noConfusionstatement · cited by 0
- CStarAlgebra.recOnstatement · cited by 0
- RCLike.mk.noConfusionstatement · cited by 0