Theorems · Theorem · ring theory
Subalgebra.mem_saturation_of_mul_mem_left
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
{s : Subalgebra R S} {M : Submonoid S} {H : M ≤ s.toSubmonoid} {x y : S},
x * y ∈ s.saturation M H → x ∈ M → y ∈ s.saturation M H- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- Subalgebrastatement and proof · cited by 1,353
- Eq.leproof · cited by 605
- Subsemiring.toSubmonoidstatement and proof · cited by 153
- Subalgebra.toSubsemiringstatement and proof · cited by 115
- Subalgebra.saturationstatement and proof · cited by 9
- Subalgebra.saturation_saturationproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.mem_saturation_of_mul_mem_rightproof · cited by 0