Theorems · Theorem · commutative algebra
IsAdjoinRoot.lift_self
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {f : Polynomial R}
(h : IsAdjoinRoot S f), h.lift (algebraMap R S) h.root ⋯ = RingHom.id S- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- RingHom.extproof · cited by 331
- IsAdjoinRootstatement and proof · cited by 61
- IsAdjoinRoot.rootstatement · cited by 34
- IsAdjoinRoot.liftstatement · cited by 11
- IsAdjoinRoot.aeval_root_selfstatement · cited by 4
- IsAdjoinRoot.lift_self_applyproof · cited by 1
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