Theorems · Theorem · commutative algebra
Ideal.IsTwoSided.mul_mem_of_left
∀ {α : Type u} {inst : Semiring α} {I : Ideal α} [self : I.IsTwoSided] {a : α} (b : α), a ∈ I → a * b ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
- Assumes
- Ideal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsTwoSidedstatement and proof · cited by 179
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.mul_mem_rightproof · cited by 71