Theorems · Theorem · commutative algebra
Module.Finite.iff_cofg_bot
∀ (R : Type u_1) [inst : Ring R] (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M], ⊥.CoFG ↔ Module.Finite R M
A module is finite if and only if the bottom submodule is CoFG.
- Defined in
- Mathlib.RingTheory.Finiteness.Cofinite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites10
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 · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- Module.Finitestatement and proof · cited by 1,032
- Submodule.CoFGstatement and proof · cited by 28
- Module.Finite.equivproof · cited by 20
- Submodule.quotEquivOfEqBotproof · cited by 15
- Submodule.CoFG.of_finiteproof · cited by 1
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