Theorems · Theorem · linear algebra
Submodule.Quotient.mk_surjective
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M),
Function.Surjective Submodule.Quotient.mk- Defined in
- Mathlib.LinearAlgebra.Quotient.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Submodule.Quotient.mkstatement · cited by 184
Cited by13
Results whose statement or proof uses this declaration.
- Ideal.jacobson_eq_iff_jacobson_quotient_eq_botproof · cited by 2
- AdicCompletion.of_surjective_iffproof · cited by 2
- rank_quotient_add_rank_leproof · cited by 1
- Representation.Coinvariants.mk_surjectiveproof · cited by 1
- AdicCompletion.mk_surjectiveproof · cited by 1
- Module.torsion_by_prime_power_decompositionproof · cited by 1
- Module.exists_smul_eq_zero_and_mk_eqproof · cited by 1
- QuotSMulTop.mem_annihilatorproof · cited by 1
- LinearMap.ker_eq_bot_range_liftQ_iffproof · cited by 0
- Module.Finite.of_submodule_quotientproof · cited by 0
- Submodule.exists_smul_notMem_of_rank_ltproof · cited by 0
- AdicCompletion.spanFinrank_maximalIdeal_eqproof · cited by 0