Theorems · Theorem · commutative algebra

IsSMulRegular.subsingleton_linearMap_iff

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup N]
  [inst_3 : Module R M] [inst_4 : Module R N] [IsNoetherianRing R] [Module.Finite R M] [Module.Finite R N],
  Subsingleton (N →ₗ[R] M) ↔ ∃ r ∈ Module.annihilator R N, IsSMulRegular M r

Defined in

Mathlib.RingTheory.Regular.LinearMap

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleIsNoetherianRingModule.FiniteModule.Finite