Mathlib Map

Theorems · Definition · ring theory

TwoSidedIdeal.ringCon

{R : Type u_1} → [inst : NonUnitalNonAssocRing R] → TwoSidedIdeal R → RingCon R

The congruence relation induced by this ideal.

Defined in
Mathlib.RingTheory.TwoSidedIdeal.Basic
Cited by
40 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
NonUnitalNonAssocRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

TwoSidedIdeal.matrix · cited by 10TwoSidedIdeal.matrixTwoSidedIdeal.mem_iff · cited by 9TwoSidedIdeal.mem_iffTwoSidedIdeal.mul_mem_left · cited by 8TwoSidedIdeal.mul_mem_leftTwoSidedIdeal.mul_mem_right · cited by 7TwoSidedIdeal.mul_mem_rig…TwoSidedIdeal.comap · cited by 5TwoSidedIdeal.comapTwoSidedIdeal.zero_mem · cited by 4TwoSidedIdeal.zero_memTwoSidedIdeal.op · cited by 4TwoSidedIdeal.opTwoSidedIdeal.orderIsoRingCon · cited by 4TwoSidedIdeal.orderIsoRin…TwoSidedIdeal.rel_iff · cited by 4TwoSidedIdeal.rel_iffTwoSidedIdeal.equivMatrix · cited by 4TwoSidedIdeal.equivMatrixTwoSidedIdeal.unop · cited by 4TwoSidedIdeal.unopTwoSidedIdeal.neg_mem · cited by 3TwoSidedIdeal.neg_memTwoSidedIdeal.add_mem · cited by 3TwoSidedIdeal.add_memTwoSidedIdeal.ringCon_injective · cited by 3TwoSidedIdeal.ringCon_inj…TwoSidedIdeal.ker_eq_bot · cited by 2TwoSidedIdeal.ker_eq_botNonUnitalNonAssocRing · cited by 354NonUnitalNonAssocRingRingCon · cited by 219RingConTwoSidedIdeal · cited by 151TwoSidedIdealTwoSidedIdeal.ringConCITED BYCITES

Cites3

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

Cited by47

Results whose statement or proof uses this declaration.