Theorems · Theorem · commutative algebra
IsLocalization.coeSubmodule_top
∀ {R : Type u_1} [inst : CommSemiring R] (S : Type u_2) [inst_1 : CommSemiring S] [inst_2 : Algebra R S],
IsLocalization.coeSubmodule S ⊤ = 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Idealstatement · cited by 4,748
- LinearMap.rangeproof · cited by 893
- Algebra.linearMapproof · cited by 157
- Submodule.map_topproof · cited by 105
- IsLocalization.coeSubmodulestatement · cited by 30
- Submodule.one_eq_rangeproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.coe_oneproof · cited by 14
- FractionalIdeal.isPrincipal_of_unit_of_comap_mul_span_singleton_eq_topproof · cited by 1
- FractionalIdeal.coe_inv_of_ne_zeroproof · cited by 0