Theorems · Theorem · commutative algebra
Submodule.colon_univ
∀ {R : Type u_1} [inst : Semiring R] {I : Ideal R} [I.IsTwoSided], Submodule.colon I Set.univ = I- Defined in
- Mathlib.RingTheory.Ideal.Colon
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
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.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Set.univstatement and proof · cited by 3,945
- mul_oneproof · cited by 3,885
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Submodule.colonstatement · cited by 80
- Ideal.mul_mem_rightproof · cited by 71
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.annihilator_quotientproof · cited by 4
- Ideal.isPrime_radicalproof · cited by 2
- IsAssociatedPrime.eq_radicalproof · cited by 1
- Ideal.isPrimary_finsetInfproof · cited by 1
- Ideal.le_colonproof · cited by 1
- Ideal.IsPrimary.infproof · cited by 0
- Submodule.colon_topproof · cited by 0