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Theorems · Theorem · commutative algebra

MonoidHom.map_neg

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : Monoid M] [IsMulTorsionFree M] (f : R →* M) (x : R),
  f (-x) = f x
Defined in
Mathlib.Algebra.Ring.Torsion
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
RingMonoidIsMulTorsionFree
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Around this declaration

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

Valuation.map_neg · cited by 11Valuation.map_negMonoidHom.map_sub_swap · cited by 1MonoidHom.map_sub_swapDFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingMonoid · cited by 3887MonoidMonoidHom · cited by 3629MonoidHomone_mul · cited by 2841one_mulmap_mul · cited by 1137map_mulneg_one_mul · cited by 61neg_one_mulIsMulTorsionFree · cited by 44IsMulTorsionFreeMonoidHom.map_neg_one · cited by 1MonoidHom.map_neg_oneMonoidHom.map_negCITED BYCITES

Cites9

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

Cited by2

Results whose statement or proof uses this declaration.