Theorems · Theorem · commutative algebra

Module.Invertible.leftInverse_iff_rightInverse

∀ {R : Type u} {M : Type v} {N : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N]
  [inst_3 : Module R M] [inst_4 : Module R N] [Module.Invertible R M] [Module.Invertible R N] (f : M →ₗ[R] N)
  (g : N →ₗ[R] M), Function.LeftInverse ⇑f ⇑g ↔ Function.RightInverse ⇑f ⇑g

Defined in: Mathlib.RingTheory.PicardGroup
Cited by: 0 results in Mathlib
Foundations: Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid AddCommMonoid Module Module Module.Invertible Module.Invertible

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DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement and proof · cited by 10,215
Module.Invertiblestatement and proof · cited by 41
Module.Invertible.rightInverse_of_leftInverseproof · cited by 2
Module.Invertible.leftInverse_of_rightInverseproof · cited by 1

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