Theorems · Theorem · commutative algebra
RingCon.rangeS_kerLift
∀ {M : Type u_1} {P : Type u_3} [inst : NonAssocSemiring M] [inst_1 : NonAssocSemiring P] {f : M →+* P},
(RingCon.kerLift f).rangeS = f.rangeSGiven a ring homomorphism f, the induced homomorphism
on the quotient by f's kernel has the same image as f.
- Defined in
- Mathlib.RingTheory.Congruence.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- RingCon.Quotientstatement · cited by 118
- RingCon.kerstatement · cited by 47
- RingHom.rangeSstatement · cited by 47
- RingCon.kerLiftstatement · cited by 5
- RingCon.rangeS_liftproof · cited by 2
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