Theorems · Theorem · commutative algebra
FractionalIdeal.coe_zero
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P],
↑0 = ⊥- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 7,192
- Bot.botstatement · cited by 4,720
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement · cited by 423
- Submodule.extproof · cited by 204
- FractionalIdeal.coeToSubmodulestatement · cited by 130
- FractionalIdeal.mem_zero_iffproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- FractionalIdeal.isFractional_div_of_ne_zeroproof · cited by 5
- FractionalIdeal.spanSingleton_eq_zero_iffproof · cited by 3
- FractionalIdeal.coeToSubmodule_eq_botproof · cited by 2
- FractionalIdeal.num_zero_eqproof · cited by 2
- FractionalIdeal.coeSubmoduleHomproof · cited by 2
- FractionalIdeal.extended_ne_zeroproof · cited by 1
- FractionalIdeal.isNoetherian_zeroproof · cited by 1
- FractionalIdeal.extended_zeroproof · cited by 1
- FractionalIdeal.isPrincipal.of_isPrincipal_pow_of_coprimeproof · cited by 0
- FractionalIdeal.spanFinset_eq_zeroproof · cited by 0
- FractionalIdeal.coe_natCastproof · cited by 0