Theorems · Theorem · commutative algebra
coe_subset_nonunits
∀ {α : Type u_2} [inst : Semiring α] {I : Ideal α}, I ≠ ⊤ → ↑I ⊆ nonunits α- Defined in
- Mathlib.RingTheory.Ideal.Nonunits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- IsUnitproof · cited by 1,602
- nonunitsstatement · cited by 35
- Ideal.eq_top_of_isUnit_memproof · cited by 26
Cited by2
Results whose statement or proof uses this declaration.
- AlgHom.apply_mem_spectrumproof · cited by 5
- Ideal.closure_ne_topproof · cited by 1