Theorems · Theorem · commutative algebra

Module.Invertible.finrank_eq_one

∀ (R : Type u) (M : Type v) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [Module.Invertible R M] [Module.Free R M], Module.finrank R M = 1

Defined in: Mathlib.RingTheory.PicardGroup
Cited by: 2 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module Module.Invertible Module.Free

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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
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Module.finrankstatement · cited by 1,770
Module.Freestatement and proof · cited by 597
Nonempty.someproof · cited by 340
LinearEquiv.finrank_eqproof · cited by 65
Module.Invertiblestatement and proof · cited by 41
Module.Invertible.free_iff_linearEquivproof · cited by 3
CommSemiring.finrank_selfproof · cited by 3

Cited by2

Results whose statement or proof uses this declaration.

Module.Invertible.rank_eq_oneproof · cited by 0
Module.free_of_isStablyFree_of_invertibleproof · cited by 0