Theorems · Theorem · commutative algebra

Module.Finite.of_pi

∀ {R : Type u_1} [inst : Semiring R] {ι : Type u_6} (M : ι → Type u_7) [inst_1 : (i : ι) → AddCommMonoid (M i)]
  [inst_2 : (i : ι) → Module R (M i)] [Module.Finite R ((i : ι) → M i)] (i : ι), Module.Finite R (M i)

Defined in: Mathlib.RingTheory.Finiteness.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring AddCommMonoid Module Module.Finite

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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
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Module.Finitestatement and proof · cited by 1,032
LinearMap.projproof · cited by 71
Module.Finite.of_surjectiveproof · cited by 29
LinearMap.proj_surjectiveproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Module.Finite.pi_iffproof · cited by 0