Theorems · Theorem · ring theory
RingHom.map_zero
∀ {α : Type u_2} {β : Type u_3} {x : NonAssocSemiring α} {x_1 : NonAssocSemiring β} (f : α →+* β), f 0 = 0Ring homomorphisms map zero to zero.
- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- map_zeroproof · cited by 1,614
- NonAssocSemiringstatement and proof · cited by 805
Cited by47
Results whose statement or proof uses this declaration.
- MvPolynomial.eval₂_addproof · cited by 23
- Algebra.adjoin_inductionproof · cited by 22
- MvPolynomial.coeff_mapproof · cited by 13
- MvPolynomial.eval₂_monomialproof · cited by 13
- Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroproof · cited by 9
- CliffordAlgebra.inductionproof · cited by 8
- LinearMap.BilinForm.dualSubmodule_span_of_basisproof · cited by 7
- FractionalIdeal.count_well_definedproof · cited by 5
- FractionalIdeal.dual_ne_zeroproof · cited by 5
- Valuation.Integers.dvd_of_leproof · cited by 4
- RingHom.isIntegralElem_zeroproof · cited by 3
- IsConjRoot.eq_zero_of_injectiveproof · cited by 3