Theorems · Theorem · commutative algebra
FractionalIdeal.eq_zero_or_one
∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [IsFractionRing K L]
(I : FractionalIdeal (nonZeroDivisors K) L), I = 0 ∨ I = 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- map_mulproof · cited by 1,137
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- FractionalIdealstatement and proof · cited by 423
- Algebra.smul_defproof · cited by 287
- IsLocalization.mk'proof · cited by 218
- Submodule.smul_memproof · cited by 204
- FractionalIdeal.coeToSubmoduleproof · cited by 130
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.eq_zero_or_one_of_isFieldproof · cited by 0