Theorems · Theorem · group theory
AddMonoidHom.mem_ker
∀ {G : Type u_1} [inst : AddGroup G] {M : Type u_7} [inst_1 : AddZeroClass M] {f : G →+ M} {x : G}, x ∈ f.ker ↔ f x = 0- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- AddGroupAddZeroClass
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.
- DFunLike.coestatement · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- AddMonoidHom.kerstatement · cited by 158
Cited by26
Results whose statement or proof uses this declaration.
- AddSubgroup.comap_map_eqproof · cited by 8
- AddMonoidHom.isOpenQuotientMap_of_isQuotientMapproof · cited by 3
- AddMonoidHom.ker_eq_bot_of_cancelproof · cited by 2
- AddMonoidHom.eq_iffproof · cited by 2
- NormedAddGroupHom.mem_kerproof · cited by 2
- IsAddTorsion.extension_closedproof · cited by 2
- NumberField.Units.dirichletUnitTheorem.logEmbedding_kerproof · cited by 2
- AddSubgroup.mem_goursatFstproof · cited by 2
- AddSubgroup.mem_goursatSndproof · cited by 2
- AddGroupExtension.Section.add_add_add_neg_mem_range_inlproof · cited by 1
- AddGroupExtension.Section.add_neg_add_add_mem_range_inlproof · cited by 1
- AddGroupExtension.Section.add_neg_mem_range_inlproof · cited by 1