Theorems · Theorem · commutative algebra

Module.Finite.of_submodule_quotient

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (N : Submodule R M)
  [Module.Finite R ↥N] [Module.Finite R (M ⧸ N)], Module.Finite R M

Defined in: Mathlib.RingTheory.Finiteness.Finsupp
Cited by: 0 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module Module.Finite Module.Finite

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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
Module.Finitestatement and proof · cited by 1,032
Submodule.Quotient.mk_surjectiveproof · cited by 13
LinearMap.exact_subtype_mkQproof · cited by 10
Module.Finite.of_exactproof · cited by 1

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