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Theorems · Definition · ring theory

Subsemiring.opEquiv

{R : Type u_2} → [inst : NonAssocSemiring R] → Subsemiring R ≃o Subsemiring Rᵐᵒᵖ

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

Defined in
Mathlib.Algebra.Ring.Subsemiring.MulOpposite
Cited by
18 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
NonAssocSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Subsemiring.unop_injective · cited by 2Subsemiring.unop_injectiveSubsemiring.op_injective · cited by 2Subsemiring.op_injectiveSubsemiring.unop_bot · cited by 1Subsemiring.unop_botSubsemiring.op_bot · cited by 1Subsemiring.op_botSubsemiring.op_inj · cited by 1Subsemiring.op_injSubsemiring.op_sInf · cited by 1Subsemiring.op_sInfSubsemiring.unop_iInf · cited by 0Subsemiring.unop_iInfSubsemiring.unop_iSup · cited by 0Subsemiring.unop_iSupSubsemiring.unop_inj · cited by 0Subsemiring.unop_injSubsemiring.unop_sInf · cited by 0Subsemiring.unop_sInfSubsemiring.unop_sSup · cited by 0Subsemiring.unop_sSupSubsemiring.unop_sup · cited by 0Subsemiring.unop_supSubsemiring.opEquiv_apply · cited by 0Subsemiring.opEquiv_applySubsemiring.opEquiv_symm_apply · cited by 0Subsemiring.opEquiv_symm_…Subsemiring.op_iInf · cited by 0Subsemiring.op_iInfMulOpposite · cited by 1135MulOppositeOrderIso · cited by 874OrderIsoNonAssocSemiring · cited by 805NonAssocSemiringSubsemiring · cited by 456SubsemiringSubsemiring.op · cited by 43Subsemiring.opSubsemiring.unop · cited by 26Subsemiring.unopSubsemiring.op_unop · cited by 1Subsemiring.op_unopSubsemiring.unop_op · cited by 0Subsemiring.unop_opSubsemiring.op_le_op_iff · cited by 0Subsemiring.op_le_op_iffSubsemiring.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.