Theorems · Definition · commutative algebra
IsLocalization.coeSubmodule
{R : Type u_1} →
[inst : CommSemiring R] →
(S : Type u_2) → [inst_1 : CommSemiring S] → [inst_2 : Algebra R S] → Ideal R → Submodule R SMap from ideals of R to submodules of S induced by f.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Submodule.mapproof · cited by 614
- Algebra.linearMapproof · cited by 157
Cited by31
Results whose statement or proof uses this declaration.
- FractionalIdeal.coeIdealproof · cited by 109
- NumberField.absNorm_differentIdealproof · cited by 4
- IsLocalization.coeSubmodule_le_coeSubmodulestatement · cited by 4
- IsFractionRing.coeSubmodule_le_coeSubmodulestatement · cited by 3
- IsLocalization.coeSubmodule_spanstatement · cited by 3
- IsLocalization.coeSubmodule_topstatement · cited by 3
- IsFractionRing.coeSubmodule_isPrincipalstatement · cited by 2
- IsLocalization.mem_coeSubmodulestatement · cited by 2
- IsLocalization.coeSubmodule_isPrincipalstatement and proof · cited by 2
- FractionalIdeal.coe_one_eq_coeSubmodule_topstatement · cited by 1
- mem_coeSubmodule_conductorstatement · cited by 1
- FractionalIdeal.coe_coeIdealstatement · cited by 1