Theorems · Theorem · commutative algebra
FractionalIdeal.coe_one
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P],
↑1 = 1- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Submodulestatement and proof · cited by 7,192
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement · cited by 423
- FractionalIdeal.coeToSubmodulestatement · cited by 130
- IsLocalization.coeSubmodule_topproof · cited by 3
- FractionalIdeal.coe_one_eq_coeSubmodule_topproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- coeIdeal_differentIdealproof · cited by 8
- FractionalIdeal.coe_dual_oneproof · cited by 7
- NumberField.absNorm_differentIdealproof · cited by 4
- FractionalIdeal.one_leproof · cited by 2
- FractionalIdeal.coeSubmoduleHomproof · cited by 2
- FractionalIdeal.den_mem_invproof · cited by 1
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1
- FractionalIdeal.isPrincipal_of_unit_of_comap_mul_span_singleton_eq_topproof · cited by 1
- pow_sub_one_dvd_differentIdeal_auxproof · cited by 1
- FractionalIdeal.dual_eq_dual_mul_dualproof · cited by 1
- FractionalIdeal.mul_one_div_le_oneproof · cited by 1
- FractionalIdeal.le_self_mul_one_divproof · cited by 1