Theorems · Theorem · commutative algebra
FractionalIdeal.mem_one_iff
∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
{x : P}, x ∈ 1 ↔ ∃ x', (algebraMap R P) x' = x- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 12 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement · cited by 423
- Algebra.linearMapproof · cited by 157
Cited by12
Results whose statement or proof uses this declaration.
- FractionalIdeal.spanSingleton_oneproof · cited by 12
- FractionalIdeal.le_one_iff_exists_coeIdealproof · cited by 5
- FractionalIdeal.coeIdeal_le_oneproof · cited by 5
- NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_ltproof · cited by 2
- FractionalIdeal.le_one_of_extendedHom_le_oneproof · cited by 2
- FractionalIdeal.not_inv_le_one_of_ne_botproof · cited by 2
- FractionalIdeal.one_mem_oneproof · cited by 1
- Ideal.exist_integer_multiples_notMemproof · cited by 1
- NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt'proof · cited by 1
- FractionalIdeal.coe_ideal_mul_invproof · cited by 1
- NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discrproof · cited by 1
- NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_leproof · cited by 0