Mathlib Map

Theorems · Definition · ring theory

Subring.opEquiv

{R : Type u_2} → [inst : NonAssocRing R] → Subring R ≃o Subring Rᵐᵒᵖ

A subring S of R determines a subring S.op of the opposite ring Rᵐᵒᵖ.

Defined in
Mathlib.Algebra.Ring.Subring.MulOpposite
Cited by
18 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Quot.sound
Assumes
NonAssocRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Subring.op_injective · cited by 2Subring.op_injectiveSubring.unop_injective · cited by 2Subring.unop_injectiveSubring.op_sInf · cited by 1Subring.op_sInfSubring.unop_bot · cited by 1Subring.unop_botSubring.op_bot · cited by 1Subring.op_botSubring.op_inj · cited by 1Subring.op_injSubring.op_sSup · cited by 0Subring.op_sSupSubring.op_sup · cited by 0Subring.op_supSubring.unop_iInf · cited by 0Subring.unop_iInfSubring.unop_iSup · cited by 0Subring.unop_iSupSubring.unop_inj · cited by 0Subring.unop_injSubring.unop_sInf · cited by 0Subring.unop_sInfSubring.unop_sSup · cited by 0Subring.unop_sSupSubring.unop_sup · cited by 0Subring.unop_supSubring.opEquiv_apply · cited by 0Subring.opEquiv_applyMulOpposite · cited by 1135MulOppositeOrderIso · cited by 874OrderIsoSubring · cited by 602SubringNonAssocRing · cited by 483NonAssocRingSubring.op · cited by 32Subring.opSubring.unop · cited by 25Subring.unopSubring.op_unop · cited by 1Subring.op_unopSubring.op_le_op_iff · cited by 0Subring.op_le_op_iffSubring.unop_op · cited by 0Subring.unop_opSubring.opEquivCITED BYCITES

Cites9

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

Cited by18

Results whose statement or proof uses this declaration.