Theorems · Definition · commutative algebra
Subring.centerToMulOpposite
{R : Type u} → [inst : NonAssocRing R] → ↥(Subring.center R) ≃+* ↥(Subring.center Rᵐᵒᵖ)The center of a (not necessarily associative) ring is isomorphic to the center of its opposite.
- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingEquivstatement · cited by 1,147
- MulOppositestatement · cited by 1,135
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Subring.centerstatement · cited by 28
- NonUnitalSubsemiring.centerToMulOppositeproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subring.centerToMulOpposite_apply_coestatement and proof · cited by 0
- Subring.centerToMulOpposite_symm_apply_coestatement and proof · cited by 0