Theorems · Theorem · ring theory
TrivSqZeroExt.mem_kerIdeal_iff_inr
∀ (R : Type u_1) (M : Type u_2) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : Module Rᵐᵒᵖ M] [inst_4 : IsCentralScalar R M] (x : TrivSqZeroExt R M), x ∈ TrivSqZeroExt.kerIdeal R M ↔ x = TrivSqZeroExt.inr x.snd
- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
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Cites14
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
- Idealstatement · cited by 4,748
- MulOppositestatement and proof · cited by 1,135
- TrivSqZeroExtstatement and proof · cited by 180
- TrivSqZeroExt.fstproof · cited by 96
- TrivSqZeroExt.sndstatement and proof · cited by 83
- TrivSqZeroExt.inrstatement and proof · cited by 59
- IsCentralScalarstatement and proof · cited by 39
- TrivSqZeroExt.fst_inrproof · cited by 4
- TrivSqZeroExt.kerIdealstatement · cited by 2
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