Theorems · Theorem · commutative algebra
RingHom.mem_range
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R →+* S} {y : S},
y ∈ f.range ↔ ∃ x, f x = y- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- RingHom.rangestatement · cited by 138
Cited by10
Results whose statement or proof uses this declaration.
- IsPurelyInseparable.elemExponent_le_of_pow_memproof · cited by 3
- RingHom.rangeRestrict_surjectiveproof · cited by 3
- RingHom.mem_range_selfproof · cited by 3
- JacobsonNoether.exists_pow_mem_center_of_inseparableproof · cited by 2
- Ideal.eq_zero_of_polynomial_mem_map_rangeproof · cited by 1
- IsPurelyInseparable.elemExponent_defproof · cited by 1
- gal_X_pow_sub_C_isSolvable_auxproof · cited by 1
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1
- Subring.mem_botproof · cited by 0
- Polynomial.isIntegrallyClosed_iff'proof · cited by 0