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Theorems · Theorem · field theory

IsConjRoot.isIntegral

∀ {R : Type u_1} {A : Type u_5} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {x y : A},
  IsIntegral R x → IsConjRoot R x y → IsIntegral R y

If y is a conjugate root of an integral element x over R, then y is also integral over R.

Defined in
Mathlib.FieldTheory.Minpoly.IsConjRoot
Cited by
1 results in Mathlib
Foundations
Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingRingAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsConjRoot.isIntegral_iff · cited by 0IsConjRoot.isIntegral_iffCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463Ringminpoly · cited by 439minpolyIsIntegral · cited by 427IsIntegralminpoly.aeval · cited by 91minpoly.aevalminpoly.monic · cited by 81minpoly.monicIsConjRoot · cited by 43IsConjRootIsConjRoot.isIntegralCITED BYCITES

Cites8

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Cited by1

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