Theorems · Theorem · ring theory
RingHom.codomain_trivial
∀ {α : Type u_2} {β : Type u_3} {x : NonAssocSemiring α} {x_1 : NonAssocSemiring β} (f : α →+* β) [h : Subsingleton α],
Subsingleton β- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subsingleton
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.
- RingHomstatement and proof · cited by 10,189
- Nontrivialproof · cited by 2,416
- NonAssocSemiringstatement and proof · cited by 805
- subsingleton_or_nontrivialproof · cited by 161
- not_nontrivial_iff_subsingletonproof · cited by 23
- RingHom.domain_nontrivialproof · cited by 20
Cited by7
Results whose statement or proof uses this declaration.
- IsLocalization.rank_eqproof · cited by 7
- IsIntegral.exists_multiple_integral_of_isLocalizationproof · cited by 7
- IsBaseChange.lift_rank_eqproof · cited by 3
- Algebra.IsFiniteSplit.of_subsingletonproof · cited by 1
- isNilpotent_tensor_residueField_iffproof · cited by 1
- isIntegral_of_isIntegralElem_of_monic_of_natDegree_ltproof · cited by 1
- Algebra.subsingletonproof · cited by 0