Theorems · Theorem · ring theory
IsSemisimpleModule.annihilator_isRadical
∀ (M : Type u_4) [inst : AddCommGroup M] (R : Type u_6) [inst_1 : CommRing R] [inst_2 : Module R M] [IsSemisimpleModule R M], (Module.annihilator R M).IsRadical
The annihilator of a semisimple module over a commutative ring is a radical ideal.
- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submoduleproof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Idealproof · cited by 4,748
- IsSimpleModuleproof · cited by 114
- IsSemisimpleModulestatement and proof · cited by 67
- Module.annihilatorstatement · cited by 61
- Ideal.IsMaximal.isPrimeproof · cited by 53
- Submodule.annihilatorproof · cited by 42
Cited by4
Results whose statement or proof uses this declaration.
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
- Module.End.IsSemisimple.minpoly_squarefreeproof · cited by 2
- Module.End.IsSemisimple.aevalproof · cited by 1
- Module.End.eq_zero_of_isNilpotent_isSemisimpleproof · cited by 1