Theorems · Theorem · ring theory
simple_of_finrank_eq_one
∀ {R : Type u_1} [inst : Ring R] {k : Type u_3} [inst_1 : Field k] [inst_2 : Algebra k R] {V : ModuleCat R},
Module.finrank k ↑V = 1 → CategoryTheory.Simple VAny k-algebra module which is 1-dimensional over k is simple.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Module.finrankstatement and proof · cited by 1,770
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement and proof · cited by 997
- CategoryTheory.Simplestatement · cited by 39
- isSimpleModule_iffproof · cited by 12
- ModuleCat.moduleOfAlgebraModulestatement · cited by 2
- simple_iff_isSimpleModule'proof · cited by 2
- is_simple_module_of_finrank_eq_oneproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.