Mathlib Map

Theorems · Theorem · commutative algebra

RingHom.IsIntegralElem.neg

∀ {R : Type u_1} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S) {x : S},
  f.IsIntegralElem x → f.IsIntegralElem (-x)
Defined in
Mathlib.RingTheory.IntegralClosure.Algebra.Basic
Cited by
3 results in Mathlib
Foundations
Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

RingHom.IsIntegralElem.sub · cited by 2IsIntegralElem.subRingHom.IsIntegralElem.of_neg · cited by 1IsIntegralElem.of_negRingHom.IsIntegralElem.neg_iff · cited by 0IsIntegralElem.neg_iffCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomSubring.closure · cited by 78Subring.closureRingHom.IsIntegralElem · cited by 33RingHom.IsIntegralElemSubring.subset_closure · cited by 18Subring.subset_closureRingHom.IsIntegralElem.of_mem_closure · cited by 4IsIntegralElem.of_mem_clo…Subring.neg_mem · cited by 3Subring.neg_memIsIntegralElem.negCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.